7.em_for_lmar.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "36e8fdcb",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "from itertools import product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8fbea531",
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_a(N, ksi, zeta_1, var_1, zeta_2, var_2):\n",
    "    '''\n",
    "    generate a of size N with given parameters\n",
    "    '''\n",
    "    a = np.zeros(N)\n",
    "    p1 = np.zeros(N)\n",
    "    p2 = np.zeros(N)\n",
    "\n",
    "    for i in range(N):\n",
    "\n",
    "        # find lags of a_t\n",
    "        if i>=2:\n",
    "            a_lag1 = a[i-1]\n",
    "            a_lag2 = a[i-2]\n",
    "        elif i==1:\n",
    "            a_lag1 = a[i-1]\n",
    "            a_lag2 = 0\n",
    "        elif i==0:\n",
    "            a_lag1 = 0\n",
    "            a_lag2 = 0\n",
    "\n",
    "        # solve probability equation\n",
    "        p1[i] = (np.exp(np.dot(ksi, [1, abs(a_lag1), abs(a_lag2)])) / \n",
    "                 (1 + np.exp(np.dot(ksi, [1, abs(a_lag1), abs(a_lag2)]))))\n",
    "        p2[i] = 1-p1[i]\n",
    "\n",
    "        # calculate means of two regimes\n",
    "        e1 = np.dot(zeta_1, np.array([1, a_lag1, a_lag2]))\n",
    "        e2 = np.dot(zeta_2, np.array([1, a_lag1]))\n",
    "\n",
    "\n",
    "        regime = np.random.choice([1,2], p=[p1[i],p2[i]])\n",
    "        if regime==1:\n",
    "            a[i] = stats.norm(loc=e1, scale=np.sqrt(var_1)).rvs()\n",
    "        else:\n",
    "            a[i] = stats.norm(loc=e2, scale=np.sqrt(var_2)).rvs()\n",
    "    \n",
    "    return a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d3b7ac62",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 500 # number of datapoints to generate\n",
    "ksi = [-1.3, 0.6, 0.3]\n",
    "zeta_1 = [0, 0.6, -0.2]\n",
    "var_1 = 1\n",
    "zeta_2 = [0, 1.5]\n",
    "var_2 = 3\n",
    "\n",
    "np.random.seed(5)\n",
    "a = generate_a(N, ksi, zeta_1, var_1, zeta_2, var_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8059eae4",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f26b9d37b80>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(18,6))\n",
    "plt.plot(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "948e7665",
   "metadata": {},
   "source": [
    "# EM Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2ed49936",
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://www.askpython.com/python/examples/detection-removal-outliers-in-python\n",
    "def remove_outliers(data):\n",
    "    data = np.array(data)\n",
    "    \n",
    "    # don't do anything if there is no variability in data\n",
    "    if data.std() < 0.001:\n",
    "        return data\n",
    "    \n",
    "    p75, p25 = np.percentile(data, [75,25])\n",
    "    iqr = p75-p25\n",
    "    max_val = p75 + 1.5*iqr\n",
    "    min_val = p25 - 1.5*iqr\n",
    "    data[data>max_val] = np.nan\n",
    "    data[data<min_val] = np.nan\n",
    "    \n",
    "    return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "94c82e88",
   "metadata": {},
   "outputs": [],
   "source": [
    "def outer(x):\n",
    "    '''\n",
    "    calculate outer product of a vector x with itself\n",
    "    '''\n",
    "    return np.outer(x,x)\n",
    "\n",
    "def em_algorithm(a, max_iter, tol):\n",
    "    '''\n",
    "    run em algorithm for max_iter iterations or until convergence\n",
    "    '''\n",
    "    \n",
    "    npdf = stats.norm.pdf\n",
    "    \n",
    "    converged = False\n",
    "    \n",
    "    while not converged:\n",
    "        try:\n",
    "            # random initial guess\n",
    "            ksi = np.random.uniform(-3,3,(3))\n",
    "            zeta_1 = np.random.uniform(-3,3,(3))\n",
    "            zeta_2 = np.random.uniform(-3,3,(2))\n",
    "            var_1 = np.random.uniform(0,6,(1))\n",
    "            var_2 = np.random.uniform(0,6,(1))\n",
    "\n",
    "            # true values\n",
    "            #ksi = np.array([-1.3,0.6,0.3])\n",
    "            #zeta_1 = np.array([0,0.6,-0.2])\n",
    "            #zeta_2 = np.array([0,1.5])\n",
    "            #var_1 = np.array([1])\n",
    "            #var_2 = np.array([3])\n",
    "\n",
    "\n",
    "            # create dataframe\n",
    "            df = pd.DataFrame(columns=['const', 'a', 'a_l1', 'a_l2', 'abs_l1', 'abs_l2', 'p1', 'p2', \n",
    "                                       'tau1', 'tau2', 'e1', 'e2'])\n",
    "            df['a'] = a[2:]\n",
    "            df['a_l1'] = a[1:-1]\n",
    "            df['a_l2'] = a[:-2]\n",
    "            df['abs_l1'] = abs(df['a_l1'])\n",
    "            df['abs_l2'] = abs(df['a_l2'])\n",
    "            df['const'] = 1\n",
    "\n",
    "\n",
    "            for s in range(max_iter):\n",
    "                # E-step\n",
    "                # solve for mixing probabilities\n",
    "                num = np.exp((df[['const', 'abs_l1', 'abs_l2']] * ksi).sum(axis=1))\n",
    "                denom = (1 + np.exp((df[['const', 'abs_l1', 'abs_l2']] * ksi).sum(axis=1)))\n",
    "                df['p1'] = num/denom\n",
    "                df['p2'] = 1 - df['p1']\n",
    "\n",
    "                # calculate e\n",
    "                df['e1'] = df['a'] - (zeta_1 * df[['const', 'a_l1', 'a_l2']]).sum(axis=1)\n",
    "                df['e2'] = df['a'] - (zeta_2 * df[['const', 'a_l1']]).sum(axis=1)\n",
    "\n",
    "                # calculate tau\n",
    "                sigma_1 = np.sqrt(var_1)\n",
    "                sigma_2 = np.sqrt(var_2)\n",
    "                denom = ((df['p1'] / sigma_1) * stats.norm.pdf(df['e1'] / sigma_1) + \n",
    "                         (df['p2'] / sigma_2) * stats.norm.pdf(df['e2'] / sigma_2))\n",
    "                df['tau1'] = (df['p1'] / sigma_1) * stats.norm.pdf(df['e1'] / sigma_1) / denom\n",
    "                df['tau2'] = (df['p2'] / sigma_2) * stats.norm.pdf(df['e2'] / sigma_2) / denom\n",
    "\n",
    "\n",
    "                # M-step\n",
    "\n",
    "                # compute ksi\n",
    "                dr_dksi = df[['const', 'abs_l1', 'abs_l2']]\n",
    "                dQ_dksi = (np.tile((df['tau1'] - df['p1']), (3,1)).T * dr_dksi).sum().values\n",
    "                df['dr_dksi^2'] = df[['const', 'abs_l1', 'abs_l2']].apply(outer, axis=1).apply(np.array)\n",
    "                d2Q_dksi2 = -(df['p1'] * df['p2'] * df['dr_dksi^2']).sum()\n",
    "                new_ksi = ksi - np.linalg.inv(d2Q_dksi2) @ dQ_dksi\n",
    "\n",
    "                # compute zeta\n",
    "                df['de1_dzeta1^2'] = df[['const', 'a_l1', 'a_l2']].apply(outer, axis=1).apply(np.array)\n",
    "                df['de2_dzeta2^2'] = df[['const', 'a_l1']].apply(outer, axis=1).apply(np.array)\n",
    "                zeta1_sum1 = (df['tau1'] * df['de1_dzeta1^2']).sum()\n",
    "                zeta2_sum1 = (df['tau2'] * df['de2_dzeta2^2']).sum()\n",
    "                zeta1_sum2 = (-np.tile(df['tau1'] * df['a'], (3,1)).T * -df[['const', 'a_l1', 'a_l2']]).sum().values\n",
    "                zeta2_sum2 = (-np.tile(df['tau2'] * df['a'], (2,1)).T * -df[['const', 'a_l1']]).sum().values\n",
    "                new_zeta_1 = np.linalg.inv(zeta1_sum1) @ zeta1_sum2\n",
    "                new_zeta_2 = np.linalg.inv(zeta2_sum1) @ zeta2_sum2\n",
    "\n",
    "                # compute variance\n",
    "                sigma1_sum2 = (df['tau1'] * (df['a'] + np.dot(-df[['const', 'a_l1', 'a_l2']], new_zeta_1))**2).sum()\n",
    "                sigma2_sum2 = (df['tau2'] * (df['a'] + np.dot(-df[['const', 'a_l1']], new_zeta_2))**2).sum()\n",
    "                new_var_1 = 1/df['tau1'].sum() * sigma1_sum2\n",
    "                new_var_2 = 1/df['tau2'].sum() * sigma2_sum2\n",
    "\n",
    "                # calculate the difference between old and new values of parameters\n",
    "                delta_ksi = np.sum(abs(new_ksi - ksi))\n",
    "                delta_zeta_1 = np.sum(abs(new_zeta_1 - zeta_1))\n",
    "                delta_zeta_2 = np.sum(abs(new_zeta_2 - zeta_2))\n",
    "                delta_var_1 = np.sum(abs(new_var_1 - var_1))\n",
    "                delta_var_2 = np.sum(abs(new_var_2 - var_2))\n",
    "\n",
    "                # update parameters\n",
    "                ksi = new_ksi\n",
    "                zeta_1 = new_zeta_1\n",
    "                zeta_2 = new_zeta_2\n",
    "                var_1 = new_var_1\n",
    "                var_2 = new_var_2\n",
    "\n",
    "                # calculate total difference between old and new parameters\n",
    "                delta_total = delta_ksi + delta_zeta_1 + delta_zeta_2 + delta_var_1 + delta_var_2\n",
    "\n",
    "                # check convergence\n",
    "                if delta_total < tol:\n",
    "                    print('Converged at iteration ', s)\n",
    "                    converged = True\n",
    "                    break\n",
    "\n",
    "                # if any parameter is nan, stop\n",
    "                nansum = (np.isnan(ksi).sum() + np.isnan(zeta_1).sum() + np.isnan(zeta_2).sum() + \n",
    "                          np.isnan(var_1).sum() + np.isnan(var_2).sum())\n",
    "                if nansum != 0:\n",
    "                    break\n",
    "\n",
    "            if not converged:\n",
    "                print(f'Algorithm not converged')\n",
    "                print('Repeating with different initital values')\n",
    "        except:\n",
    "            continue\n",
    "\n",
    "    # calculate Q\n",
    "    Q_sum1 = (df['tau1'] * (np.log(df['p1']) - 1/2*np.log(var_1) - df['e1']**2 / (2 * var_1))).sum()\n",
    "    Q_sum2 = (df['tau2'] * (np.log(df['p2']) - 1/2*np.log(var_2) - df['e2']**2 / (2 * var_2))).sum()\n",
    "    Q = Q_sum1 + Q_sum2\n",
    "        \n",
    "    return ksi, zeta_1, var_1, zeta_2, var_2, Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d50b67c3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Running sim  0\n",
      "Converged at iteration  43\n",
      "\n",
      "Running sim  1\n",
      "Converged at iteration  23\n",
      "\n",
      "Running sim  2\n",
      "Converged at iteration  56\n",
      "\n",
      "Running sim  3\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  4\n",
      "Converged at iteration  156\n",
      "\n",
      "Running sim  5\n",
      "Converged at iteration  32\n",
      "\n",
      "Running sim  6\n",
      "Converged at iteration  111\n",
      "\n",
      "Running sim  7\n",
      "Converged at iteration  61\n",
      "\n",
      "Running sim  8\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  11\n",
      "\n",
      "Running sim  9\n",
      "Converged at iteration  23\n",
      "\n",
      "Running sim  10\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  11\n",
      "Converged at iteration  23\n",
      "\n",
      "Running sim  12\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  33\n",
      "\n",
      "Running sim  13\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  13\n",
      "\n",
      "Running sim  14\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  56\n",
      "\n",
      "Running sim  15\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  29\n",
      "\n",
      "Running sim  16\n",
      "Converged at iteration  41\n",
      "\n",
      "Running sim  17\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  18\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  29\n",
      "\n",
      "Running sim  19\n",
      "Converged at iteration  19\n",
      "\n",
      "Running sim  20\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  17\n",
      "\n",
      "Running sim  21\n",
      "Converged at iteration  18\n",
      "\n",
      "Running sim  22\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  64\n",
      "\n",
      "Running sim  23\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  16\n",
      "\n",
      "Running sim  24\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  36\n",
      "\n",
      "Running sim  25\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  34\n",
      "\n",
      "Running sim  26\n",
      "Converged at iteration  21\n",
      "\n",
      "Running sim  27\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  25\n",
      "\n",
      "Running sim  28\n",
      "Converged at iteration  39\n",
      "\n",
      "Running sim  29\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  30\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  44\n",
      "\n",
      "Running sim  31\n",
      "Converged at iteration  51\n",
      "\n",
      "Running sim  32\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  13\n",
      "\n",
      "Running sim  33\n",
      "Converged at iteration  29\n",
      "\n",
      "Running sim  34\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  35\n",
      "Converged at iteration  79\n",
      "\n",
      "Running sim  36\n",
      "Converged at iteration  22\n",
      "\n",
      "Running sim  37\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  38\n",
      "Converged at iteration  49\n",
      "\n",
      "Running sim  39\n",
      "Converged at iteration  50\n",
      "\n",
      "Running sim  40\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  41\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  42\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  43\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  44\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  31\n",
      "\n",
      "Running sim  45\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  49\n",
      "\n",
      "Running sim  46\n",
      "Converged at iteration  22\n",
      "\n",
      "Running sim  47\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  48\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  26\n",
      "\n",
      "Running sim  49\n",
      "Converged at iteration  20\n",
      "\n",
      "Running sim  50\n",
      "Converged at iteration  24\n",
      "\n",
      "Running sim  51\n",
      "Converged at iteration  22\n",
      "\n",
      "Running sim  52\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  53\n",
      "Converged at iteration  19\n",
      "\n",
      "Running sim  54\n",
      "Converged at iteration  29\n",
      "\n",
      "Running sim  55\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  56\n",
      "Converged at iteration  23\n",
      "\n",
      "Running sim  57\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  58\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  18\n",
      "\n",
      "Running sim  59\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  5\n",
      "\n",
      "Running sim  60\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  40\n",
      "\n",
      "Running sim  61\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  18\n",
      "\n",
      "Running sim  62\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  63\n",
      "Converged at iteration  21\n",
      "\n",
      "Running sim  64\n",
      "Converged at iteration  38\n",
      "\n",
      "Running sim  65\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  66\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  67\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  68\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  69\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  5\n",
      "\n",
      "Running sim  70\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  71\n",
      "Converged at iteration  15\n",
      "\n",
      "Running sim  72\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  73\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  74\n",
      "Converged at iteration  18\n",
      "\n",
      "Running sim  75\n",
      "Converged at iteration  151\n",
      "\n",
      "Running sim  76\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  77\n",
      "Converged at iteration  70\n",
      "\n",
      "Running sim  78\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  56\n",
      "\n",
      "Running sim  79\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  66\n",
      "\n",
      "Running sim  80\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  38\n",
      "\n",
      "Running sim  81\n",
      "Converged at iteration  38\n",
      "\n",
      "Running sim  82\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  83\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  84\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  28\n",
      "\n",
      "Running sim  85\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  86\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  36\n",
      "\n",
      "Running sim  87\n",
      "Converged at iteration  56\n",
      "\n",
      "Running sim  88\n",
      "Converged at iteration  31\n",
      "\n",
      "Running sim  89\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  49\n",
      "\n",
      "Running sim  90\n",
      "Converged at iteration  19\n",
      "\n",
      "Running sim  91\n",
      "Converged at iteration  36\n",
      "\n",
      "Running sim  92\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  29\n",
      "\n",
      "Running sim  93\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  94\n",
      "\n",
      "Running sim  94\n",
      "Converged at iteration  23\n",
      "\n",
      "Running sim  95\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  25\n",
      "\n",
      "Running sim  96\n",
      "Converged at iteration  35\n",
      "\n",
      "Running sim  97\n",
      "Converged at iteration  32\n",
      "\n",
      "Running sim  98\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  20\n",
      "\n",
      "Running sim  99\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  74\n",
      "\n",
      "Running sim  100\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  23\n",
      "\n",
      "Running sim  101\n",
      "Converged at iteration  26\n",
      "\n",
      "Running sim  102\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  103\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  104\n",
      "Converged at iteration  29\n",
      "\n",
      "Running sim  105\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  38\n",
      "\n",
      "Running sim  106\n",
      "Converged at iteration  32\n",
      "\n",
      "Running sim  107\n",
      "Converged at iteration  15\n",
      "\n",
      "Running sim  108\n",
      "Converged at iteration  52\n",
      "\n",
      "Running sim  109\n",
      "Converged at iteration  65\n",
      "\n",
      "Running sim  110\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  111\n",
      "Converged at iteration  24\n",
      "\n",
      "Running sim  112\n",
      "Converged at iteration  82\n",
      "\n",
      "Running sim  113\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  114\n",
      "Converged at iteration  24\n",
      "\n",
      "Running sim  115\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  116\n",
      "Converged at iteration  13\n",
      "\n",
      "Running sim  117\n",
      "Converged at iteration  48\n",
      "\n",
      "Running sim  118\n",
      "Converged at iteration  19\n",
      "\n",
      "Running sim  119\n",
      "Converged at iteration  19\n",
      "\n",
      "Running sim  120\n",
      "Converged at iteration  23\n",
      "\n",
      "Running sim  121\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  18\n",
      "\n",
      "Running sim  122\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  78\n",
      "\n",
      "Running sim  123\n",
      "Converged at iteration  174\n",
      "\n",
      "Running sim  124\n",
      "Converged at iteration  26\n",
      "\n",
      "Running sim  125\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  24\n",
      "\n",
      "Running sim  126\n",
      "Converged at iteration  49\n",
      "\n",
      "Running sim  127\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  128\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  129\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  15\n",
      "\n",
      "Running sim  130\n",
      "Converged at iteration  46\n",
      "\n",
      "Running sim  131\n",
      "Converged at iteration  21\n",
      "\n",
      "Running sim  132\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  133\n",
      "Converged at iteration  44\n",
      "\n",
      "Running sim  134\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  57\n",
      "\n",
      "Running sim  135\n",
      "Converged at iteration  80\n",
      "\n",
      "Running sim  136\n",
      "Converged at iteration  23\n",
      "\n",
      "Running sim  137\n",
      "Converged at iteration  36\n",
      "\n",
      "Running sim  138\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  139\n",
      "Converged at iteration  79\n",
      "\n",
      "Running sim  140\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  22\n",
      "\n",
      "Running sim  141\n",
      "Converged at iteration  24\n",
      "\n",
      "Running sim  142\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  24\n",
      "\n",
      "Running sim  143\n",
      "Converged at iteration  29\n",
      "\n",
      "Running sim  144\n",
      "Converged at iteration  24\n",
      "\n",
      "Running sim  145\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  36\n",
      "\n",
      "Running sim  146\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  48\n",
      "\n",
      "Running sim  147\n",
      "Converged at iteration  16\n",
      "\n",
      "Running sim  148\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  60\n",
      "\n",
      "Running sim  149\n",
      "Converged at iteration  41\n",
      "\n",
      "Running sim  150\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  32\n",
      "\n",
      "Running sim  151\n",
      "Converged at iteration  16\n",
      "\n",
      "Running sim  152\n",
      "Converged at iteration  30\n",
      "\n",
      "Running sim  153\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  21\n",
      "\n",
      "Running sim  154\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  32\n",
      "\n",
      "Running sim  155\n",
      "Converged at iteration  25\n",
      "\n",
      "Running sim  156\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  41\n",
      "\n",
      "Running sim  157\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  158\n",
      "Converged at iteration  37\n",
      "\n",
      "Running sim  159\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  160\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  31\n",
      "\n",
      "Running sim  161\n",
      "Converged at iteration  38\n",
      "\n",
      "Running sim  162\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  39\n",
      "\n",
      "Running sim  163\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  164\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  20\n",
      "\n",
      "Running sim  165\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  166\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  167\n",
      "Converged at iteration  33\n",
      "\n",
      "Running sim  168\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  169\n",
      "Converged at iteration  25\n",
      "\n",
      "Running sim  170\n",
      "Converged at iteration  22\n",
      "\n",
      "Running sim  171\n",
      "Converged at iteration  24\n",
      "\n",
      "Running sim  172\n",
      "Converged at iteration  64\n",
      "\n",
      "Running sim  173\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  174\n",
      "Converged at iteration  39\n",
      "\n",
      "Running sim  175\n",
      "Converged at iteration  15\n",
      "\n",
      "Running sim  176\n",
      "Converged at iteration  16\n",
      "\n",
      "Running sim  177\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  32\n",
      "\n",
      "Running sim  178\n",
      "Converged at iteration  34\n",
      "\n",
      "Running sim  179\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  19\n",
      "\n",
      "Running sim  180\n",
      "Converged at iteration  15\n",
      "\n",
      "Running sim  181\n",
      "Converged at iteration  59\n",
      "\n",
      "Running sim  182\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  183\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  184\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  185\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  31\n",
      "\n",
      "Running sim  186\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  92\n",
      "\n",
      "Running sim  187\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  188\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  41\n",
      "\n",
      "Running sim  189\n",
      "Converged at iteration  46\n",
      "\n",
      "Running sim  190\n",
      "Converged at iteration  35\n",
      "\n",
      "Running sim  191\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  192\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  193\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  15\n",
      "\n",
      "Running sim  194\n",
      "Converged at iteration  36\n",
      "\n",
      "Running sim  195\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  34\n",
      "\n",
      "Running sim  196\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  20\n",
      "\n",
      "Running sim  197\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  16\n",
      "\n",
      "Running sim  198\n",
      "Converged at iteration  41\n",
      "\n",
      "Running sim  199\n",
      "Converged at iteration  18\n",
      "\n",
      "Running sim  200\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  201\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  23\n",
      "\n",
      "Running sim  202\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  203\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  16\n",
      "\n",
      "Running sim  204\n",
      "Converged at iteration  35\n",
      "\n",
      "Running sim  205\n",
      "Converged at iteration  45\n",
      "\n",
      "Running sim  206\n",
      "Converged at iteration  22\n",
      "\n",
      "Running sim  207\n",
      "Converged at iteration  28\n",
      "\n",
      "Running sim  208\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  209\n",
      "Converged at iteration  35\n",
      "\n",
      "Running sim  210\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  37\n",
      "\n",
      "Running sim  211\n",
      "Converged at iteration  43\n",
      "\n",
      "Running sim  212\n",
      "Converged at iteration  31\n",
      "\n",
      "Running sim  213\n",
      "Converged at iteration  3\n",
      "\n",
      "Running sim  214\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  26\n",
      "\n",
      "Running sim  215\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  216\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  217\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  218\n",
      "Converged at iteration  159\n",
      "\n",
      "Running sim  219\n",
      "Converged at iteration  23\n",
      "\n",
      "Running sim  220\n",
      "Converged at iteration  13\n",
      "\n",
      "Running sim  221\n",
      "Converged at iteration  53\n",
      "\n",
      "Running sim  222\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  25\n",
      "\n",
      "Running sim  223\n",
      "Converged at iteration  35\n",
      "\n",
      "Running sim  224\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  178\n",
      "\n",
      "Running sim  225\n",
      "Converged at iteration  22\n",
      "\n",
      "Running sim  226\n",
      "Converged at iteration  24\n",
      "\n",
      "Running sim  227\n",
      "Converged at iteration  20\n",
      "\n",
      "Running sim  228\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  229\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  230\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  35\n",
      "\n",
      "Running sim  231\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  62\n",
      "\n",
      "Running sim  232\n",
      "Converged at iteration  81\n",
      "\n",
      "Running sim  233\n",
      "Converged at iteration  50\n",
      "\n",
      "Running sim  234\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  20\n",
      "\n",
      "Running sim  235\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  37\n",
      "\n",
      "Running sim  236\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  237\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  238\n",
      "Converged at iteration  47\n",
      "\n",
      "Running sim  239\n",
      "Converged at iteration  26\n",
      "\n",
      "Running sim  240\n",
      "Converged at iteration  50\n",
      "\n",
      "Running sim  241\n",
      "Converged at iteration  3\n",
      "\n",
      "Running sim  242\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  17\n",
      "\n",
      "Running sim  243\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  244\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  245\n",
      "Converged at iteration  69\n",
      "\n",
      "Running sim  246\n",
      "Converged at iteration  29\n",
      "\n",
      "Running sim  247\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  23\n",
      "\n",
      "Running sim  248\n",
      "Converged at iteration  62\n",
      "\n",
      "Running sim  249\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  250\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  251\n",
      "Converged at iteration  31\n",
      "\n",
      "Running sim  252\n",
      "Converged at iteration  40\n",
      "\n",
      "Running sim  253\n",
      "Converged at iteration  28\n",
      "\n",
      "Running sim  254\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  255\n",
      "Converged at iteration  15\n",
      "\n",
      "Running sim  256\n",
      "Converged at iteration  59\n",
      "\n",
      "Running sim  257\n",
      "Converged at iteration  19\n",
      "\n",
      "Running sim  258\n",
      "Converged at iteration  20\n",
      "\n",
      "Running sim  259\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  260\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  3\n",
      "\n",
      "Running sim  261\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  61\n",
      "\n",
      "Running sim  262\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  63\n",
      "\n",
      "Running sim  263\n",
      "Converged at iteration  30\n",
      "\n",
      "Running sim  264\n",
      "Converged at iteration  30\n",
      "\n",
      "Running sim  265\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  42\n",
      "\n",
      "Running sim  266\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  16\n",
      "\n",
      "Running sim  267\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  268\n",
      "Converged at iteration  85\n",
      "\n",
      "Running sim  269\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  270\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  9\n",
      "\n",
      "Running sim  271\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  272\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  273\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  22\n",
      "\n",
      "Running sim  274\n",
      "Converged at iteration  28\n",
      "\n",
      "Running sim  275\n",
      "Converged at iteration  20\n",
      "\n",
      "Running sim  276\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  26\n",
      "\n",
      "Running sim  277\n",
      "Converged at iteration  37\n",
      "\n",
      "Running sim  278\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  37\n",
      "\n",
      "Running sim  279\n",
      "Converged at iteration  28\n",
      "\n",
      "Running sim  280\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  37\n",
      "\n",
      "Running sim  281\n",
      "Converged at iteration  24\n",
      "\n",
      "Running sim  282\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  75\n",
      "\n",
      "Running sim  283\n",
      "Converged at iteration  18\n",
      "\n",
      "Running sim  284\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged at iteration  29\n",
      "\n",
      "Running sim  285\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  29\n",
      "\n",
      "Running sim  286\n",
      "Converged at iteration  40\n",
      "\n",
      "Running sim  287\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  288\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  54\n",
      "\n",
      "Running sim  289\n",
      "Converged at iteration  19\n",
      "\n",
      "Running sim  290\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  20\n",
      "\n",
      "Running sim  291\n",
      "Converged at iteration  38\n",
      "\n",
      "Running sim  292\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  39\n",
      "\n",
      "Running sim  293\n",
      "Converged at iteration  26\n",
      "\n",
      "Running sim  294\n",
      "Converged at iteration  24\n",
      "\n",
      "Running sim  295\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  296\n",
      "Converged at iteration  25\n",
      "\n",
      "Running sim  297\n",
      "Converged at iteration  41\n",
      "\n",
      "Running sim  298\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  299\n",
      "Converged at iteration  13\n"
     ]
    }
   ],
   "source": [
    "delta_0s = []\n",
    "delta_1s = []\n",
    "delta_2s = []\n",
    "phi_10s = []\n",
    "phi_11s = []\n",
    "phi_12s = []\n",
    "phi_20s = []\n",
    "phi_21s = []\n",
    "var_1s = []\n",
    "var_2s = []\n",
    "Qs = []\n",
    "\n",
    "max_iter=200\n",
    "tol = 0.1\n",
    "\n",
    "N = 500 # number of datapoints to generate\n",
    "N_sim = 300 # number of simulations to run\n",
    "\n",
    "# parameters used to generate a\n",
    "ksi = [-1.3, 0.6, 0.3]\n",
    "zeta_1 = [0, 0.6, -0.2]\n",
    "var_1 = 1\n",
    "zeta_2 = [0, 1.5]\n",
    "var_2 = 3\n",
    "\n",
    "\n",
    "for s in range(N_sim):\n",
    "    print()\n",
    "    print('Running sim ', s)\n",
    "    \n",
    "    # generate a\n",
    "    np.random.seed(123+s)\n",
    "    a = generate_a(N, ksi, zeta_1, var_1, zeta_2, var_2)\n",
    "    \n",
    "    # run EM algorithm\n",
    "    ksi_hat, zeta_1_hat, var_1_hat, zeta_2_hat, var_2_hat, Q = em_algorithm(a, max_iter, tol)\n",
    "    \n",
    "    # save results\n",
    "    delta_0s.append(ksi_hat[0])\n",
    "    delta_1s.append(ksi_hat[1])\n",
    "    delta_2s.append(ksi_hat[2])\n",
    "    phi_10s.append(zeta_1_hat[0])\n",
    "    phi_11s.append(zeta_1_hat[1])\n",
    "    phi_12s.append(zeta_1_hat[2])\n",
    "    phi_20s.append(zeta_2_hat[0])\n",
    "    phi_21s.append(zeta_2_hat[1])\n",
    "    var_1s.append(var_1_hat)\n",
    "    var_2s.append(var_2_hat)\n",
    "    Qs.append(Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b95cc244",
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://www.askpython.com/python/examples/detection-removal-outliers-in-python\n",
    "def remove_outliers(data):\n",
    "    data = np.array(data)\n",
    "    \n",
    "    # don't do anything if there is no variability in data\n",
    "    if data.std() < 0.001:\n",
    "        return data\n",
    "    \n",
    "    p75, p25 = np.percentile(data, [75,25])\n",
    "    iqr = p75-p25\n",
    "    max_val = p75 + 1.5*iqr\n",
    "    min_val = p25 - 1.5*iqr\n",
    "    data[data>max_val] = np.nan\n",
    "    data[data<min_val] = np.nan\n",
    "    \n",
    "    return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fab83bc1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>True value</th>\n",
       "      <th>Mean of estimates</th>\n",
       "      <th>SD of estimates</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>$\\sigma_1^2$</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.074724</td>\n",
       "      <td>1.054503</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{1,0}$</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.007341</td>\n",
       "      <td>0.120649</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{1,1}$</th>\n",
       "      <td>0.6</td>\n",
       "      <td>1.066887</td>\n",
       "      <td>0.480513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{1,2}$</th>\n",
       "      <td>-0.2</td>\n",
       "      <td>-0.137320</td>\n",
       "      <td>0.129651</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\sigma_2^2$</th>\n",
       "      <td>3.0</td>\n",
       "      <td>2.135976</td>\n",
       "      <td>0.965487</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{2,0}$</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.001278</td>\n",
       "      <td>0.107729</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{2,1}$</th>\n",
       "      <td>1.5</td>\n",
       "      <td>0.874741</td>\n",
       "      <td>0.486525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\delta_0$</th>\n",
       "      <td>-1.3</td>\n",
       "      <td>0.027557</td>\n",
       "      <td>1.565362</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\delta_1$</th>\n",
       "      <td>0.6</td>\n",
       "      <td>0.031473</td>\n",
       "      <td>0.719762</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\delta_2$</th>\n",
       "      <td>0.3</td>\n",
       "      <td>-0.109673</td>\n",
       "      <td>0.542525</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              True value  Mean of estimates  SD of estimates\n",
       "$\\sigma_1^2$         1.0           2.074724         1.054503\n",
       "$\\phi_{1,0}$         0.0           0.007341         0.120649\n",
       "$\\phi_{1,1}$         0.6           1.066887         0.480513\n",
       "$\\phi_{1,2}$        -0.2          -0.137320         0.129651\n",
       "$\\sigma_2^2$         3.0           2.135976         0.965487\n",
       "$\\phi_{2,0}$         0.0           0.001278         0.107729\n",
       "$\\phi_{2,1}$         1.5           0.874741         0.486525\n",
       "$\\delta_0$          -1.3           0.027557         1.565362\n",
       "$\\delta_1$           0.6           0.031473         0.719762\n",
       "$\\delta_2$           0.3          -0.109673         0.542525"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "index = [r'$\\sigma_1^2$', r'$\\phi_{1,0}$', r'$\\phi_{1,1}$', \n",
    "         r'$\\phi_{1,2}$', r'$\\sigma_2^2$', r'$\\phi_{2,0}$', r'$\\phi_{2,1}$', r'$\\delta_0$', r'$\\delta_1$', \n",
    "         r'$\\delta_2$']\n",
    "columns = ['True value', 'Mean of estimates', 'SD of estimates']\n",
    "results_df = pd.DataFrame(index=index, columns=columns)\n",
    "results_df['True value'] = [1, 0, 0.6, -0.2, 3, 0, 1.5, -1.3, 0.6, 0.3]\n",
    "parameters = [var_1s, phi_10s, phi_11s, phi_12s, var_2s, phi_20s, phi_21s, \n",
    "              delta_0s, delta_1s, delta_2s]\n",
    "    \n",
    "results_df['Mean of estimates'] = [np.nanmean(remove_outliers(x)) for x in parameters]\n",
    "results_df['SD of estimates'] = [np.nanstd(remove_outliers(x)) for x in parameters]\n",
    "results_df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e5a6eb4",
   "metadata": {},
   "source": [
    "# Zeta_2, var_2 known"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "50730c7c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def em_algorithm(a, max_iter, tol):\n",
    "    '''\n",
    "    run em algorithm for max_iter iterations or until convergence\n",
    "    '''\n",
    "    \n",
    "    npdf = stats.norm.pdf\n",
    "    \n",
    "    converged = False\n",
    "    \n",
    "    while not converged:\n",
    "        try:\n",
    "            # random initial guess\n",
    "            ksi = np.random.uniform(-3,3,(3))\n",
    "            zeta_1 = np.random.uniform(-3,3,(3))\n",
    "            #zeta_2 = np.random.uniform(-3,3,(2))\n",
    "            var_1 = np.random.uniform(0,6,(1))\n",
    "            #var_2 = np.random.uniform(0,6,(1))\n",
    "\n",
    "            # true values\n",
    "            #ksi = np.array([-1.3,0.6,0.3])\n",
    "            #zeta_1 = np.array([0,0.6,-0.2])\n",
    "            zeta_2 = np.array([0,1.5])\n",
    "            #var_1 = np.array([1])\n",
    "            var_2 = np.array([3])\n",
    "\n",
    "\n",
    "            # create dataframe\n",
    "            df = pd.DataFrame(columns=['const', 'a', 'a_l1', 'a_l2', 'abs_l1', 'abs_l2', 'p1', 'p2', \n",
    "                                       'tau1', 'tau2', 'e1', 'e2'])\n",
    "            df['a'] = a[2:]\n",
    "            df['a_l1'] = a[1:-1]\n",
    "            df['a_l2'] = a[:-2]\n",
    "            df['abs_l1'] = abs(df['a_l1'])\n",
    "            df['abs_l2'] = abs(df['a_l2'])\n",
    "            df['const'] = 1\n",
    "\n",
    "\n",
    "            for s in range(max_iter):\n",
    "                # E-step\n",
    "                # solve for mixing probabilities\n",
    "                num = np.exp((df[['const', 'abs_l1', 'abs_l2']] * ksi).sum(axis=1))\n",
    "                denom = (1 + np.exp((df[['const', 'abs_l1', 'abs_l2']] * ksi).sum(axis=1)))\n",
    "                df['p1'] = num/denom\n",
    "                df['p2'] = 1 - df['p1']\n",
    "\n",
    "                # calculate e\n",
    "                df['e1'] = df['a'] - (zeta_1 * df[['const', 'a_l1', 'a_l2']]).sum(axis=1)\n",
    "                df['e2'] = df['a'] - (zeta_2 * df[['const', 'a_l1']]).sum(axis=1)\n",
    "\n",
    "                # calculate tau\n",
    "                sigma_1 = np.sqrt(var_1)\n",
    "                sigma_2 = np.sqrt(var_2)\n",
    "                denom = ((df['p1'] / sigma_1) * stats.norm.pdf(df['e1'] / sigma_1) + \n",
    "                         (df['p2'] / sigma_2) * stats.norm.pdf(df['e2'] / sigma_2))\n",
    "                df['tau1'] = (df['p1'] / sigma_1) * stats.norm.pdf(df['e1'] / sigma_1) / denom\n",
    "                df['tau2'] = (df['p2'] / sigma_2) * stats.norm.pdf(df['e2'] / sigma_2) / denom\n",
    "\n",
    "\n",
    "                # M-step\n",
    "\n",
    "                # compute ksi\n",
    "                dr_dksi = df[['const', 'abs_l1', 'abs_l2']]\n",
    "                dQ_dksi = (np.tile((df['tau1'] - df['p1']), (3,1)).T * dr_dksi).sum().values\n",
    "                df['dr_dksi^2'] = df[['const', 'abs_l1', 'abs_l2']].apply(outer, axis=1).apply(np.array)\n",
    "                d2Q_dksi2 = -(df['p1'] * df['p2'] * df['dr_dksi^2']).sum()\n",
    "                new_ksi = ksi - np.linalg.inv(d2Q_dksi2) @ dQ_dksi\n",
    "\n",
    "                # compute zeta\n",
    "                df['de1_dzeta1^2'] = df[['const', 'a_l1', 'a_l2']].apply(outer, axis=1).apply(np.array)\n",
    "                df['de2_dzeta2^2'] = df[['const', 'a_l1']].apply(outer, axis=1).apply(np.array)\n",
    "                zeta1_sum1 = (df['tau1'] * df['de1_dzeta1^2']).sum()\n",
    "                zeta2_sum1 = (df['tau2'] * df['de2_dzeta2^2']).sum()\n",
    "                zeta1_sum2 = (-np.tile(df['tau1'] * df['a'], (3,1)).T * -df[['const', 'a_l1', 'a_l2']]).sum().values\n",
    "                zeta2_sum2 = (-np.tile(df['tau2'] * df['a'], (2,1)).T * -df[['const', 'a_l1']]).sum().values\n",
    "                new_zeta_1 = np.linalg.inv(zeta1_sum1) @ zeta1_sum2\n",
    "                new_zeta_2 = np.linalg.inv(zeta2_sum1) @ zeta2_sum2\n",
    "\n",
    "                # compute variance\n",
    "                sigma1_sum2 = (df['tau1'] * (df['a'] + np.dot(-df[['const', 'a_l1', 'a_l2']], new_zeta_1))**2).sum()\n",
    "                sigma2_sum2 = (df['tau2'] * (df['a'] + np.dot(-df[['const', 'a_l1']], new_zeta_2))**2).sum()\n",
    "                new_var_1 = 1/df['tau1'].sum() * sigma1_sum2\n",
    "                new_var_2 = 1/df['tau2'].sum() * sigma2_sum2\n",
    "\n",
    "                # calculate the difference between old and new values of parameters\n",
    "                delta_ksi = np.sum(abs(new_ksi - ksi))\n",
    "                delta_zeta_1 = np.sum(abs(new_zeta_1 - zeta_1))\n",
    "                delta_zeta_2 = np.sum(abs(new_zeta_2 - zeta_2))\n",
    "                delta_var_1 = np.sum(abs(new_var_1 - var_1))\n",
    "                delta_var_2 = np.sum(abs(new_var_2 - var_2))\n",
    "\n",
    "                # update parameters\n",
    "                ksi = new_ksi\n",
    "                zeta_1 = new_zeta_1\n",
    "                #zeta_2 = new_zeta_2\n",
    "                var_1 = new_var_1\n",
    "                #var_2 = new_var_2\n",
    "\n",
    "                # calculate total difference between old and new parameters\n",
    "                delta_total = delta_ksi + delta_zeta_1 + delta_var_1 \n",
    "\n",
    "                # check convergence\n",
    "                if delta_total < tol:\n",
    "                    print('Converged at iteration ', s)\n",
    "                    converged = True\n",
    "                    break\n",
    "\n",
    "                # if any parameter is nan, stop\n",
    "                nansum = (np.isnan(ksi).sum() + np.isnan(zeta_1).sum() + np.isnan(zeta_2).sum() + \n",
    "                          np.isnan(var_1).sum() + np.isnan(var_2).sum())\n",
    "                if nansum != 0:\n",
    "                    break\n",
    "\n",
    "            if not converged:\n",
    "                print(f'Algorithm not converged')\n",
    "                print('Repeating with different initital values')\n",
    "        except:\n",
    "            continue\n",
    "\n",
    "    # calculate Q\n",
    "    Q_sum1 = (df['tau1'] * (np.log(df['p1']) - 1/2*np.log(var_1) - df['e1']**2 / (2 * var_1))).sum()\n",
    "    Q_sum2 = (df['tau2'] * (np.log(df['p2']) - 1/2*np.log(var_2) - df['e2']**2 / (2 * var_2))).sum()\n",
    "    Q = Q_sum1 + Q_sum2\n",
    "        \n",
    "    return ksi, zeta_1, var_1, zeta_2, var_2, Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "08995db4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Running sim  0\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  1\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  2\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  3\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  4\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  5\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  6\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  7\n",
      "Converged at iteration  15\n",
      "\n",
      "Running sim  8\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  9\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  10\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  11\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  12\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  13\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  14\n",
      "Converged at iteration  21\n",
      "\n",
      "Running sim  15\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  16\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  17\n",
      "Converged at iteration  15\n",
      "\n",
      "Running sim  18\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  19\n",
      "Converged at iteration  16\n",
      "\n",
      "Running sim  20\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  21\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  22\n",
      "Converged at iteration  51\n",
      "\n",
      "Running sim  23\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: divide by zero encountered in log\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  24\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  25\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  26\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  27\n",
      "Converged at iteration  141\n",
      "\n",
      "Running sim  28\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  29\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  30\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  31\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  32\n",
      "Converged at iteration  16\n",
      "\n",
      "Running sim  33\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  34\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  35\n",
      "Converged at iteration  43\n",
      "\n",
      "Running sim  36\n",
      "Converged at iteration  15\n",
      "\n",
      "Running sim  37\n",
      "Converged at iteration  4\n",
      "\n",
      "Running sim  38\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  39\n",
      "Converged at iteration  16\n",
      "\n",
      "Running sim  40\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  41\n",
      "Converged at iteration  19\n",
      "\n",
      "Running sim  42\n",
      "Converged at iteration  25\n",
      "\n",
      "Running sim  43\n",
      "Converged at iteration  18\n",
      "\n",
      "Running sim  44\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  4\n",
      "\n",
      "Running sim  45\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  15\n",
      "\n",
      "Running sim  46\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  47\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  48\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  49\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  50\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  51\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  52\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  53\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  54\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  55\n",
      "Converged at iteration  21\n",
      "\n",
      "Running sim  56\n",
      "Converged at iteration  13\n",
      "\n",
      "Running sim  57\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  58\n",
      "Converged at iteration  13\n",
      "\n",
      "Running sim  59\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  60\n",
      "Converged at iteration  24\n",
      "\n",
      "Running sim  61\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  62\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  63\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  64\n",
      "Converged at iteration  31\n",
      "\n",
      "Running sim  65\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  66\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  67\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  68\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  69\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  70\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  71\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  72\n",
      "Converged at iteration  41\n",
      "\n",
      "Running sim  73\n",
      "Converged at iteration  40\n",
      "\n",
      "Running sim  74\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  75\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  76\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  77\n",
      "Converged at iteration  13\n",
      "\n",
      "Running sim  78\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  79\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  80\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  81\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  82\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  83\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  84\n",
      "Converged at iteration  21\n",
      "\n",
      "Running sim  85\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  86\n",
      "Converged at iteration  18\n",
      "\n",
      "Running sim  87\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  88\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  89\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  90\n",
      "Converged at iteration  15\n",
      "\n",
      "Running sim  91\n",
      "Converged at iteration  13\n",
      "\n",
      "Running sim  92\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  93\n",
      "Converged at iteration  16\n",
      "\n",
      "Running sim  94\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  95\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  96\n",
      "Converged at iteration  44\n",
      "\n",
      "Running sim  97\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  98\n",
      "Converged at iteration  13\n",
      "\n",
      "Running sim  99\n",
      "Converged at iteration  46\n"
     ]
    }
   ],
   "source": [
    "delta_0s = []\n",
    "delta_1s = []\n",
    "delta_2s = []\n",
    "phi_10s = []\n",
    "phi_11s = []\n",
    "phi_12s = []\n",
    "phi_20s = []\n",
    "phi_21s = []\n",
    "var_1s = []\n",
    "var_2s = []\n",
    "Qs = []\n",
    "\n",
    "max_iter=200\n",
    "tol = 0.1\n",
    "\n",
    "N = 500 # number of datapoints to generate\n",
    "N_sim = 100 # number of simulations to run\n",
    "\n",
    "# parameters used to generate a\n",
    "ksi = [-1.3, 0.6, 0.3]\n",
    "zeta_1 = [0, 0.6, -0.2]\n",
    "var_1 = 1\n",
    "zeta_2 = [0, 1.5]\n",
    "var_2 = 3\n",
    "\n",
    "\n",
    "for s in range(N_sim):\n",
    "    print()\n",
    "    print('Running sim ', s)\n",
    "    \n",
    "    # generate a\n",
    "    np.random.seed(123+s)\n",
    "    a = generate_a(N, ksi, zeta_1, var_1, zeta_2, var_2)\n",
    "    \n",
    "    # run EM algorithm\n",
    "    ksi_hat, zeta_1_hat, var_1_hat, zeta_2_hat, var_2_hat, Q = em_algorithm(a, max_iter, tol)\n",
    "    \n",
    "    # save results\n",
    "    delta_0s.append(ksi_hat[0])\n",
    "    delta_1s.append(ksi_hat[1])\n",
    "    delta_2s.append(ksi_hat[2])\n",
    "    phi_10s.append(zeta_1_hat[0])\n",
    "    phi_11s.append(zeta_1_hat[1])\n",
    "    phi_12s.append(zeta_1_hat[2])\n",
    "    phi_20s.append(zeta_2_hat[0])\n",
    "    phi_21s.append(zeta_2_hat[1])\n",
    "    var_1s.append(var_1_hat)\n",
    "    var_2s.append(var_2_hat)\n",
    "    Qs.append(Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7294eccd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>True value</th>\n",
       "      <th>Mean of estimates</th>\n",
       "      <th>SD of estimates</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>$\\sigma_1^2$</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.959523</td>\n",
       "      <td>0.118305</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{1,0}$</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000287</td>\n",
       "      <td>0.070615</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{1,1}$</th>\n",
       "      <td>0.6</td>\n",
       "      <td>0.595160</td>\n",
       "      <td>0.042240</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{1,2}$</th>\n",
       "      <td>-0.2</td>\n",
       "      <td>-0.198208</td>\n",
       "      <td>0.042244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\sigma_2^2$</th>\n",
       "      <td>3.0</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{2,0}$</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{2,1}$</th>\n",
       "      <td>1.5</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\delta_0$</th>\n",
       "      <td>-1.3</td>\n",
       "      <td>-1.407010</td>\n",
       "      <td>0.474070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\delta_1$</th>\n",
       "      <td>0.6</td>\n",
       "      <td>0.642940</td>\n",
       "      <td>0.175884</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\delta_2$</th>\n",
       "      <td>0.3</td>\n",
       "      <td>0.289288</td>\n",
       "      <td>0.123607</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              True value  Mean of estimates  SD of estimates\n",
       "$\\sigma_1^2$         1.0           0.959523         0.118305\n",
       "$\\phi_{1,0}$         0.0           0.000287         0.070615\n",
       "$\\phi_{1,1}$         0.6           0.595160         0.042240\n",
       "$\\phi_{1,2}$        -0.2          -0.198208         0.042244\n",
       "$\\sigma_2^2$         3.0           3.000000         0.000000\n",
       "$\\phi_{2,0}$         0.0           0.000000         0.000000\n",
       "$\\phi_{2,1}$         1.5           1.500000         0.000000\n",
       "$\\delta_0$          -1.3          -1.407010         0.474070\n",
       "$\\delta_1$           0.6           0.642940         0.175884\n",
       "$\\delta_2$           0.3           0.289288         0.123607"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "index = [r'$\\sigma_1^2$', r'$\\phi_{1,0}$', r'$\\phi_{1,1}$', \n",
    "         r'$\\phi_{1,2}$', r'$\\sigma_2^2$', r'$\\phi_{2,0}$', r'$\\phi_{2,1}$', r'$\\delta_0$', r'$\\delta_1$', \n",
    "         r'$\\delta_2$']\n",
    "columns = ['True value', 'Mean of estimates', 'SD of estimates']\n",
    "results_df = pd.DataFrame(index=index, columns=columns)\n",
    "results_df['True value'] = [1, 0, 0.6, -0.2, 3, 0, 1.5, -1.3, 0.6, 0.3]\n",
    "parameters = [var_1s, phi_10s, phi_11s, phi_12s, var_2s, phi_20s, phi_21s, \n",
    "              delta_0s, delta_1s, delta_2s]\n",
    "    \n",
    "results_df['Mean of estimates'] = [np.nanmean(remove_outliers(x)) for x in parameters]\n",
    "results_df['SD of estimates'] = [np.nanstd(remove_outliers(x)) for x in parameters]\n",
    "results_df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "554780a3",
   "metadata": {},
   "source": [
    "# Zeta_1, var_1 known"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "54d76c82",
   "metadata": {},
   "outputs": [],
   "source": [
    "def em_algorithm(a, max_iter, tol):\n",
    "    '''\n",
    "    run em algorithm for max_iter iterations or until convergence\n",
    "    '''\n",
    "    \n",
    "    npdf = stats.norm.pdf\n",
    "    \n",
    "    converged = False\n",
    "    \n",
    "    while not converged:\n",
    "        try:\n",
    "            # random initial guess\n",
    "            ksi = np.random.uniform(-3,3,(3))\n",
    "            #zeta_1 = np.random.uniform(-3,3,(3))\n",
    "            zeta_2 = np.random.uniform(-3,3,(2))\n",
    "            #var_1 = np.random.uniform(0,6,(1))\n",
    "            var_2 = np.random.uniform(0,6,(1))\n",
    "\n",
    "            # true values\n",
    "            #ksi = np.array([-1.3,0.6,0.3])\n",
    "            zeta_1 = np.array([0,0.6,-0.2])\n",
    "            #zeta_2 = np.array([0,1.5])\n",
    "            var_1 = np.array([1])\n",
    "            #var_2 = np.array([3])\n",
    "\n",
    "\n",
    "            # create dataframe\n",
    "            df = pd.DataFrame(columns=['const', 'a', 'a_l1', 'a_l2', 'abs_l1', 'abs_l2', 'p1', 'p2', \n",
    "                                       'tau1', 'tau2', 'e1', 'e2'])\n",
    "            df['a'] = a[2:]\n",
    "            df['a_l1'] = a[1:-1]\n",
    "            df['a_l2'] = a[:-2]\n",
    "            df['abs_l1'] = abs(df['a_l1'])\n",
    "            df['abs_l2'] = abs(df['a_l2'])\n",
    "            df['const'] = 1\n",
    "\n",
    "\n",
    "            for s in range(max_iter):\n",
    "                # E-step\n",
    "                # solve for mixing probabilities\n",
    "                num = np.exp((df[['const', 'abs_l1', 'abs_l2']] * ksi).sum(axis=1))\n",
    "                denom = (1 + np.exp((df[['const', 'abs_l1', 'abs_l2']] * ksi).sum(axis=1)))\n",
    "                df['p1'] = num/denom\n",
    "                df['p2'] = 1 - df['p1']\n",
    "\n",
    "                # calculate e\n",
    "                df['e1'] = df['a'] - (zeta_1 * df[['const', 'a_l1', 'a_l2']]).sum(axis=1)\n",
    "                df['e2'] = df['a'] - (zeta_2 * df[['const', 'a_l1']]).sum(axis=1)\n",
    "\n",
    "                # calculate tau\n",
    "                sigma_1 = np.sqrt(var_1)\n",
    "                sigma_2 = np.sqrt(var_2)\n",
    "                denom = ((df['p1'] / sigma_1) * stats.norm.pdf(df['e1'] / sigma_1) + \n",
    "                         (df['p2'] / sigma_2) * stats.norm.pdf(df['e2'] / sigma_2))\n",
    "                df['tau1'] = (df['p1'] / sigma_1) * stats.norm.pdf(df['e1'] / sigma_1) / denom\n",
    "                df['tau2'] = (df['p2'] / sigma_2) * stats.norm.pdf(df['e2'] / sigma_2) / denom\n",
    "\n",
    "\n",
    "                # M-step\n",
    "\n",
    "                # compute ksi\n",
    "                dr_dksi = df[['const', 'abs_l1', 'abs_l2']]\n",
    "                dQ_dksi = (np.tile((df['tau1'] - df['p1']), (3,1)).T * dr_dksi).sum().values\n",
    "                df['dr_dksi^2'] = df[['const', 'abs_l1', 'abs_l2']].apply(outer, axis=1).apply(np.array)\n",
    "                d2Q_dksi2 = -(df['p1'] * df['p2'] * df['dr_dksi^2']).sum()\n",
    "                new_ksi = ksi - np.linalg.inv(d2Q_dksi2) @ dQ_dksi\n",
    "\n",
    "                # compute zeta\n",
    "                df['de1_dzeta1^2'] = df[['const', 'a_l1', 'a_l2']].apply(outer, axis=1).apply(np.array)\n",
    "                df['de2_dzeta2^2'] = df[['const', 'a_l1']].apply(outer, axis=1).apply(np.array)\n",
    "                zeta1_sum1 = (df['tau1'] * df['de1_dzeta1^2']).sum()\n",
    "                zeta2_sum1 = (df['tau2'] * df['de2_dzeta2^2']).sum()\n",
    "                zeta1_sum2 = (-np.tile(df['tau1'] * df['a'], (3,1)).T * -df[['const', 'a_l1', 'a_l2']]).sum().values\n",
    "                zeta2_sum2 = (-np.tile(df['tau2'] * df['a'], (2,1)).T * -df[['const', 'a_l1']]).sum().values\n",
    "                new_zeta_1 = np.linalg.inv(zeta1_sum1) @ zeta1_sum2\n",
    "                new_zeta_2 = np.linalg.inv(zeta2_sum1) @ zeta2_sum2\n",
    "\n",
    "                # compute variance\n",
    "                sigma1_sum2 = (df['tau1'] * (df['a'] + np.dot(-df[['const', 'a_l1', 'a_l2']], new_zeta_1))**2).sum()\n",
    "                sigma2_sum2 = (df['tau2'] * (df['a'] + np.dot(-df[['const', 'a_l1']], new_zeta_2))**2).sum()\n",
    "                new_var_1 = 1/df['tau1'].sum() * sigma1_sum2\n",
    "                new_var_2 = 1/df['tau2'].sum() * sigma2_sum2\n",
    "\n",
    "                # calculate the difference between old and new values of parameters\n",
    "                delta_ksi = np.sum(abs(new_ksi - ksi))\n",
    "                delta_zeta_1 = np.sum(abs(new_zeta_1 - zeta_1))\n",
    "                delta_zeta_2 = np.sum(abs(new_zeta_2 - zeta_2))\n",
    "                delta_var_1 = np.sum(abs(new_var_1 - var_1))\n",
    "                delta_var_2 = np.sum(abs(new_var_2 - var_2))\n",
    "\n",
    "                # update parameters\n",
    "                ksi = new_ksi\n",
    "                #zeta_1 = new_zeta_1\n",
    "                zeta_2 = new_zeta_2\n",
    "                #var_1 = new_var_1\n",
    "                var_2 = new_var_2\n",
    "\n",
    "                # calculate total difference between old and new parameters\n",
    "                delta_total = delta_ksi + delta_zeta_2 + delta_var_2 \n",
    "\n",
    "                # check convergence\n",
    "                if delta_total < tol:\n",
    "                    print('Converged at iteration ', s)\n",
    "                    converged = True\n",
    "                    break\n",
    "\n",
    "                # if any parameter is nan, stop\n",
    "                nansum = (np.isnan(ksi).sum() + np.isnan(zeta_1).sum() + np.isnan(zeta_2).sum() + \n",
    "                          np.isnan(var_1).sum() + np.isnan(var_2).sum())\n",
    "                if nansum != 0:\n",
    "                    break\n",
    "\n",
    "            if not converged:\n",
    "                print(f'Algorithm not converged')\n",
    "                print('Repeating with different initital values')\n",
    "        except:\n",
    "            continue\n",
    "\n",
    "    # calculate Q\n",
    "    Q_sum1 = (df['tau1'] * (np.log(df['p1']) - 1/2*np.log(var_1) - df['e1']**2 / (2 * var_1))).sum()\n",
    "    Q_sum2 = (df['tau2'] * (np.log(df['p2']) - 1/2*np.log(var_2) - df['e2']**2 / (2 * var_2))).sum()\n",
    "    Q = Q_sum1 + Q_sum2\n",
    "        \n",
    "    return ksi, zeta_1, var_1, zeta_2, var_2, Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "4b153610",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Running sim  0\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  1\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  2\n",
      "Converged at iteration  2\n",
      "\n",
      "Running sim  3\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  4\n",
      "Converged at iteration  28\n",
      "\n",
      "Running sim  5\n",
      "Converged at iteration  28\n",
      "\n",
      "Running sim  6\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  7\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  8\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  9\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  10\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  11\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  12\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  13\n",
      "Converged at iteration  40\n",
      "\n",
      "Running sim  14\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  15\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  16\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  17\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  3\n",
      "\n",
      "Running sim  18\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  19\n",
      "Converged at iteration  60\n",
      "\n",
      "Running sim  20\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  21\n",
      "Converged at iteration  21\n",
      "\n",
      "Running sim  22\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  23\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  24\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  25\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  26\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  27\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  28\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  29\n",
      "Converged at iteration  63\n",
      "\n",
      "Running sim  30\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  31\n",
      "Converged at iteration  20\n",
      "\n",
      "Running sim  32\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  33\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  34\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  35\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  36\n",
      "Converged at iteration  88\n",
      "\n",
      "Running sim  37\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  38\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  39\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  40\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  41\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  42\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  16\n",
      "\n",
      "Running sim  43\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  65\n",
      "\n",
      "Running sim  44\n",
      "Converged at iteration  15\n",
      "\n",
      "Running sim  45\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  25\n",
      "\n",
      "Running sim  46\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  47\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  48\n",
      "Converged at iteration  70\n",
      "\n",
      "Running sim  49\n",
      "Converged at iteration  19\n",
      "\n",
      "Running sim  50\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  51\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  52\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  53\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  54\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  55\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  56\n",
      "Converged at iteration  15\n",
      "\n",
      "Running sim  57\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  58\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  59\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  60\n",
      "Converged at iteration  23\n",
      "\n",
      "Running sim  61\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  62\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  63\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  64\n",
      "Converged at iteration  48\n",
      "\n",
      "Running sim  65\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  66\n",
      "Converged at iteration  3\n",
      "\n",
      "Running sim  67\n",
      "Converged at iteration  30\n",
      "\n",
      "Running sim  68\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  69\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  70\n",
      "Converged at iteration  13\n",
      "\n",
      "Running sim  71\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  72\n",
      "Converged at iteration  54\n",
      "\n",
      "Running sim  73\n",
      "Converged at iteration  13\n",
      "\n",
      "Running sim  74\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  75\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  76\n",
      "Converged at iteration  13\n",
      "\n",
      "Running sim  77\n",
      "Converged at iteration  17\n",
      "\n",
      "Running sim  78\n",
      "Converged at iteration  19\n",
      "\n",
      "Running sim  79\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  80\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  81\n",
      "Converged at iteration  30\n",
      "\n",
      "Running sim  82\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  83\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  84\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  85\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  86\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  13\n",
      "\n",
      "Running sim  87\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  19\n",
      "\n",
      "Running sim  88\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  89\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  90\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  91\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  92\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  93\n",
      "Converged at iteration  21\n",
      "\n",
      "Running sim  94\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  95\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  96\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  97\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  98\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n",
      "/home/alex/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning: overflow encountered in exp\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  99\n",
      "Converged at iteration  20\n"
     ]
    }
   ],
   "source": [
    "delta_0s = []\n",
    "delta_1s = []\n",
    "delta_2s = []\n",
    "phi_10s = []\n",
    "phi_11s = []\n",
    "phi_12s = []\n",
    "phi_20s = []\n",
    "phi_21s = []\n",
    "var_1s = []\n",
    "var_2s = []\n",
    "Qs = []\n",
    "\n",
    "max_iter=200\n",
    "tol = 0.1\n",
    "\n",
    "N = 500 # number of datapoints to generate\n",
    "N_sim = 100 # number of simulations to run\n",
    "\n",
    "# parameters used to generate a\n",
    "ksi = [-1.3, 0.6, 0.3]\n",
    "zeta_1 = [0, 0.6, -0.2]\n",
    "var_1 = 1\n",
    "zeta_2 = [0, 1.5]\n",
    "var_2 = 3\n",
    "\n",
    "\n",
    "for s in range(N_sim):\n",
    "    print()\n",
    "    print('Running sim ', s)\n",
    "    \n",
    "    # generate a\n",
    "    np.random.seed(123+s)\n",
    "    a = generate_a(N, ksi, zeta_1, var_1, zeta_2, var_2)\n",
    "    \n",
    "    # run EM algorithm\n",
    "    ksi_hat, zeta_1_hat, var_1_hat, zeta_2_hat, var_2_hat, Q = em_algorithm(a, max_iter, tol)\n",
    "    \n",
    "    # save results\n",
    "    delta_0s.append(ksi_hat[0])\n",
    "    delta_1s.append(ksi_hat[1])\n",
    "    delta_2s.append(ksi_hat[2])\n",
    "    phi_10s.append(zeta_1_hat[0])\n",
    "    phi_11s.append(zeta_1_hat[1])\n",
    "    phi_12s.append(zeta_1_hat[2])\n",
    "    phi_20s.append(zeta_2_hat[0])\n",
    "    phi_21s.append(zeta_2_hat[1])\n",
    "    var_1s.append(var_1_hat)\n",
    "    var_2s.append(var_2_hat)\n",
    "    Qs.append(Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "aca14850",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>True value</th>\n",
       "      <th>Mean of estimates</th>\n",
       "      <th>SD of estimates</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>$\\sigma_1^2$</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{1,0}$</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{1,1}$</th>\n",
       "      <td>0.6</td>\n",
       "      <td>0.600000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{1,2}$</th>\n",
       "      <td>-0.2</td>\n",
       "      <td>-0.200000</td>\n",
       "      <td>5.551115e-17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\sigma_2^2$</th>\n",
       "      <td>3.0</td>\n",
       "      <td>3.037365</td>\n",
       "      <td>2.897246e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{2,0}$</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.016083</td>\n",
       "      <td>1.358192e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{2,1}$</th>\n",
       "      <td>1.5</td>\n",
       "      <td>1.487280</td>\n",
       "      <td>1.212036e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\delta_0$</th>\n",
       "      <td>-1.3</td>\n",
       "      <td>-1.242039</td>\n",
       "      <td>5.501010e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\delta_1$</th>\n",
       "      <td>0.6</td>\n",
       "      <td>0.582884</td>\n",
       "      <td>1.855568e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\delta_2$</th>\n",
       "      <td>0.3</td>\n",
       "      <td>0.272925</td>\n",
       "      <td>1.196722e-01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              True value  Mean of estimates  SD of estimates\n",
       "$\\sigma_1^2$         1.0           1.000000     0.000000e+00\n",
       "$\\phi_{1,0}$         0.0           0.000000     0.000000e+00\n",
       "$\\phi_{1,1}$         0.6           0.600000     0.000000e+00\n",
       "$\\phi_{1,2}$        -0.2          -0.200000     5.551115e-17\n",
       "$\\sigma_2^2$         3.0           3.037365     2.897246e-01\n",
       "$\\phi_{2,0}$         0.0           0.016083     1.358192e-01\n",
       "$\\phi_{2,1}$         1.5           1.487280     1.212036e-01\n",
       "$\\delta_0$          -1.3          -1.242039     5.501010e-01\n",
       "$\\delta_1$           0.6           0.582884     1.855568e-01\n",
       "$\\delta_2$           0.3           0.272925     1.196722e-01"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "index = [r'$\\sigma_1^2$', r'$\\phi_{1,0}$', r'$\\phi_{1,1}$', \n",
    "         r'$\\phi_{1,2}$', r'$\\sigma_2^2$', r'$\\phi_{2,0}$', r'$\\phi_{2,1}$', r'$\\delta_0$', r'$\\delta_1$', \n",
    "         r'$\\delta_2$']\n",
    "columns = ['True value', 'Mean of estimates', 'SD of estimates']\n",
    "results_df = pd.DataFrame(index=index, columns=columns)\n",
    "results_df['True value'] = [1, 0, 0.6, -0.2, 3, 0, 1.5, -1.3, 0.6, 0.3]\n",
    "parameters = [var_1s, phi_10s, phi_11s, phi_12s, var_2s, phi_20s, phi_21s, \n",
    "              delta_0s, delta_1s, delta_2s]\n",
    "    \n",
    "results_df['Mean of estimates'] = [np.nanmean(remove_outliers(x)) for x in parameters]\n",
    "results_df['SD of estimates'] = [np.nanstd(remove_outliers(x)) for x in parameters]\n",
    "results_df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59e83201",
   "metadata": {},
   "source": [
    "# Ksi known"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "922520bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def em_algorithm(a, max_iter, tol):\n",
    "    '''\n",
    "    run em algorithm for max_iter iterations or until convergence\n",
    "    '''\n",
    "    \n",
    "    npdf = stats.norm.pdf\n",
    "    \n",
    "    converged = False\n",
    "    \n",
    "    while not converged:\n",
    "        try:\n",
    "            # random initial guess\n",
    "            #ksi = np.random.uniform(-3,3,(3))\n",
    "            zeta_1 = np.random.uniform(-3,3,(3))\n",
    "            zeta_2 = np.random.uniform(-3,3,(2))\n",
    "            var_1 = np.random.uniform(0,6,(1))\n",
    "            var_2 = np.random.uniform(0,6,(1))\n",
    "\n",
    "            # true values\n",
    "            ksi = np.array([-1.3,0.6,0.3])\n",
    "            #zeta_1 = np.array([0,0.6,-0.2])\n",
    "            #zeta_2 = np.array([0,1.5])\n",
    "            #var_1 = np.array([1])\n",
    "            #var_2 = np.array([3])\n",
    "\n",
    "\n",
    "            # create dataframe\n",
    "            df = pd.DataFrame(columns=['const', 'a', 'a_l1', 'a_l2', 'abs_l1', 'abs_l2', 'p1', 'p2', \n",
    "                                       'tau1', 'tau2', 'e1', 'e2'])\n",
    "            df['a'] = a[2:]\n",
    "            df['a_l1'] = a[1:-1]\n",
    "            df['a_l2'] = a[:-2]\n",
    "            df['abs_l1'] = abs(df['a_l1'])\n",
    "            df['abs_l2'] = abs(df['a_l2'])\n",
    "            df['const'] = 1\n",
    "\n",
    "\n",
    "            for s in range(max_iter):\n",
    "                # E-step\n",
    "                # solve for mixing probabilities\n",
    "                num = np.exp((df[['const', 'abs_l1', 'abs_l2']] * ksi).sum(axis=1))\n",
    "                denom = (1 + np.exp((df[['const', 'abs_l1', 'abs_l2']] * ksi).sum(axis=1)))\n",
    "                df['p1'] = num/denom\n",
    "                df['p2'] = 1 - df['p1']\n",
    "\n",
    "                # calculate e\n",
    "                df['e1'] = df['a'] - (zeta_1 * df[['const', 'a_l1', 'a_l2']]).sum(axis=1)\n",
    "                df['e2'] = df['a'] - (zeta_2 * df[['const', 'a_l1']]).sum(axis=1)\n",
    "\n",
    "                # calculate tau\n",
    "                sigma_1 = np.sqrt(var_1)\n",
    "                sigma_2 = np.sqrt(var_2)\n",
    "                denom = ((df['p1'] / sigma_1) * stats.norm.pdf(df['e1'] / sigma_1) + \n",
    "                         (df['p2'] / sigma_2) * stats.norm.pdf(df['e2'] / sigma_2))\n",
    "                df['tau1'] = (df['p1'] / sigma_1) * stats.norm.pdf(df['e1'] / sigma_1) / denom\n",
    "                df['tau2'] = (df['p2'] / sigma_2) * stats.norm.pdf(df['e2'] / sigma_2) / denom\n",
    "\n",
    "\n",
    "                # M-step\n",
    "\n",
    "                # compute ksi\n",
    "                dr_dksi = df[['const', 'abs_l1', 'abs_l2']]\n",
    "                dQ_dksi = (np.tile((df['tau1'] - df['p1']), (3,1)).T * dr_dksi).sum().values\n",
    "                df['dr_dksi^2'] = df[['const', 'abs_l1', 'abs_l2']].apply(outer, axis=1).apply(np.array)\n",
    "                d2Q_dksi2 = -(df['p1'] * df['p2'] * df['dr_dksi^2']).sum()\n",
    "                new_ksi = ksi - np.linalg.inv(d2Q_dksi2) @ dQ_dksi\n",
    "\n",
    "                # compute zeta\n",
    "                df['de1_dzeta1^2'] = df[['const', 'a_l1', 'a_l2']].apply(outer, axis=1).apply(np.array)\n",
    "                df['de2_dzeta2^2'] = df[['const', 'a_l1']].apply(outer, axis=1).apply(np.array)\n",
    "                zeta1_sum1 = (df['tau1'] * df['de1_dzeta1^2']).sum()\n",
    "                zeta2_sum1 = (df['tau2'] * df['de2_dzeta2^2']).sum()\n",
    "                zeta1_sum2 = (-np.tile(df['tau1'] * df['a'], (3,1)).T * -df[['const', 'a_l1', 'a_l2']]).sum().values\n",
    "                zeta2_sum2 = (-np.tile(df['tau2'] * df['a'], (2,1)).T * -df[['const', 'a_l1']]).sum().values\n",
    "                new_zeta_1 = np.linalg.inv(zeta1_sum1) @ zeta1_sum2\n",
    "                new_zeta_2 = np.linalg.inv(zeta2_sum1) @ zeta2_sum2\n",
    "\n",
    "                # compute variance\n",
    "                sigma1_sum2 = (df['tau1'] * (df['a'] + np.dot(-df[['const', 'a_l1', 'a_l2']], new_zeta_1))**2).sum()\n",
    "                sigma2_sum2 = (df['tau2'] * (df['a'] + np.dot(-df[['const', 'a_l1']], new_zeta_2))**2).sum()\n",
    "                new_var_1 = 1/df['tau1'].sum() * sigma1_sum2\n",
    "                new_var_2 = 1/df['tau2'].sum() * sigma2_sum2\n",
    "\n",
    "                # calculate the difference between old and new values of parameters\n",
    "                delta_ksi = np.sum(abs(new_ksi - ksi))\n",
    "                delta_zeta_1 = np.sum(abs(new_zeta_1 - zeta_1))\n",
    "                delta_zeta_2 = np.sum(abs(new_zeta_2 - zeta_2))\n",
    "                delta_var_1 = np.sum(abs(new_var_1 - var_1))\n",
    "                delta_var_2 = np.sum(abs(new_var_2 - var_2))\n",
    "\n",
    "                # update parameters\n",
    "                #ksi = new_ksi\n",
    "                zeta_1 = new_zeta_1\n",
    "                zeta_2 = new_zeta_2\n",
    "                var_1 = new_var_1\n",
    "                var_2 = new_var_2\n",
    "\n",
    "                # calculate total difference between old and new parameters\n",
    "                delta_total = delta_zeta_1 + delta_var_1 + delta_zeta_2 + delta_var_2 \n",
    "\n",
    "                # check convergence\n",
    "                if delta_total < tol:\n",
    "                    print('Converged at iteration ', s)\n",
    "                    converged = True\n",
    "                    break\n",
    "\n",
    "                # if any parameter is nan, stop\n",
    "                nansum = (np.isnan(ksi).sum() + np.isnan(zeta_1).sum() + np.isnan(zeta_2).sum() + \n",
    "                          np.isnan(var_1).sum() + np.isnan(var_2).sum())\n",
    "                if nansum != 0:\n",
    "                    break\n",
    "\n",
    "            if not converged:\n",
    "                print(f'Algorithm not converged')\n",
    "                print('Repeating with different initital values')\n",
    "        except:\n",
    "            continue\n",
    "\n",
    "    # calculate Q\n",
    "    Q_sum1 = (df['tau1'] * (np.log(df['p1']) - 1/2*np.log(var_1) - df['e1']**2 / (2 * var_1))).sum()\n",
    "    Q_sum2 = (df['tau2'] * (np.log(df['p2']) - 1/2*np.log(var_2) - df['e2']**2 / (2 * var_2))).sum()\n",
    "    Q = Q_sum1 + Q_sum2\n",
    "        \n",
    "    return ksi, zeta_1, var_1, zeta_2, var_2, Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "bc7a449a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Running sim  0\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  1\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  2\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  3\n",
      "Converged at iteration  19\n",
      "\n",
      "Running sim  4\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  5\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  6\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  7\n",
      "Converged at iteration  4\n",
      "\n",
      "Running sim  8\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  9\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  10\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  11\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  12\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  13\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  14\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  15\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  16\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  17\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  18\n",
      "Converged at iteration  4\n",
      "\n",
      "Running sim  19\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  20\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  21\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  22\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  23\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  24\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  25\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  26\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  27\n",
      "Converged at iteration  27\n",
      "\n",
      "Running sim  28\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  29\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  30\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  31\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  32\n",
      "Converged at iteration  13\n",
      "\n",
      "Running sim  33\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  34\n",
      "Converged at iteration  13\n",
      "\n",
      "Running sim  35\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  36\n",
      "Converged at iteration  4\n",
      "\n",
      "Running sim  37\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  38\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  39\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  40\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  41\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  42\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  43\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  44\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  45\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  46\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  47\n",
      "Converged at iteration  16\n",
      "\n",
      "Running sim  48\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  49\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  50\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  51\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  52\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  53\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  54\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  55\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  56\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  57\n",
      "Converged at iteration  10\n",
      "\n",
      "Running sim  58\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  59\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  60\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  61\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  62\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  63\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  64\n",
      "Converged at iteration  8\n",
      "\n",
      "Running sim  65\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  66\n",
      "Converged at iteration  4\n",
      "\n",
      "Running sim  67\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  68\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  69\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  70\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  71\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  72\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  73\n",
      "Converged at iteration  11\n",
      "\n",
      "Running sim  74\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  75\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  76\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  77\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  78\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  79\n",
      "Converged at iteration  4\n",
      "\n",
      "Running sim  80\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  81\n",
      "Converged at iteration  4\n",
      "\n",
      "Running sim  82\n",
      "Converged at iteration  4\n",
      "\n",
      "Running sim  83\n",
      "Converged at iteration  14\n",
      "\n",
      "Running sim  84\n",
      "Algorithm not converged\n",
      "Repeating with different initital values\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  85\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  86\n",
      "Converged at iteration  12\n",
      "\n",
      "Running sim  87\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  88\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  89\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  90\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  91\n",
      "Converged at iteration  7\n",
      "\n",
      "Running sim  92\n",
      "Converged at iteration  5\n",
      "\n",
      "Running sim  93\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  94\n",
      "Converged at iteration  13\n",
      "\n",
      "Running sim  95\n",
      "Converged at iteration  16\n",
      "\n",
      "Running sim  96\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  97\n",
      "Converged at iteration  9\n",
      "\n",
      "Running sim  98\n",
      "Converged at iteration  6\n",
      "\n",
      "Running sim  99\n",
      "Converged at iteration  5\n"
     ]
    }
   ],
   "source": [
    "delta_0s = []\n",
    "delta_1s = []\n",
    "delta_2s = []\n",
    "phi_10s = []\n",
    "phi_11s = []\n",
    "phi_12s = []\n",
    "phi_20s = []\n",
    "phi_21s = []\n",
    "var_1s = []\n",
    "var_2s = []\n",
    "Qs = []\n",
    "\n",
    "max_iter=200\n",
    "tol = 0.1\n",
    "\n",
    "N = 500 # number of datapoints to generate\n",
    "N_sim = 100 # number of simulations to run\n",
    "\n",
    "# parameters used to generate a\n",
    "ksi = [-1.3, 0.6, 0.3]\n",
    "zeta_1 = [0, 0.6, -0.2]\n",
    "var_1 = 1\n",
    "zeta_2 = [0, 1.5]\n",
    "var_2 = 3\n",
    "\n",
    "\n",
    "for s in range(N_sim):\n",
    "    print()\n",
    "    print('Running sim ', s)\n",
    "    \n",
    "    # generate a\n",
    "    np.random.seed(123+s)\n",
    "    a = generate_a(N, ksi, zeta_1, var_1, zeta_2, var_2)\n",
    "    \n",
    "    # run EM algorithm\n",
    "    ksi_hat, zeta_1_hat, var_1_hat, zeta_2_hat, var_2_hat, Q = em_algorithm(a, max_iter, tol)\n",
    "    \n",
    "    # save results\n",
    "    delta_0s.append(ksi_hat[0])\n",
    "    delta_1s.append(ksi_hat[1])\n",
    "    delta_2s.append(ksi_hat[2])\n",
    "    phi_10s.append(zeta_1_hat[0])\n",
    "    phi_11s.append(zeta_1_hat[1])\n",
    "    phi_12s.append(zeta_1_hat[2])\n",
    "    phi_20s.append(zeta_2_hat[0])\n",
    "    phi_21s.append(zeta_2_hat[1])\n",
    "    var_1s.append(var_1_hat)\n",
    "    var_2s.append(var_2_hat)\n",
    "    Qs.append(Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "fa0eef01",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>True value</th>\n",
       "      <th>Mean of estimates</th>\n",
       "      <th>SD of estimates</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>$\\sigma_1^2$</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.944208</td>\n",
       "      <td>1.394589e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{1,0}$</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.002687</td>\n",
       "      <td>7.451277e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{1,1}$</th>\n",
       "      <td>0.6</td>\n",
       "      <td>0.666071</td>\n",
       "      <td>1.060599e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{1,2}$</th>\n",
       "      <td>-0.2</td>\n",
       "      <td>-0.199086</td>\n",
       "      <td>4.947150e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\sigma_2^2$</th>\n",
       "      <td>3.0</td>\n",
       "      <td>2.480053</td>\n",
       "      <td>7.875261e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{2,0}$</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.004845</td>\n",
       "      <td>1.360822e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi_{2,1}$</th>\n",
       "      <td>1.5</td>\n",
       "      <td>1.221861</td>\n",
       "      <td>3.929151e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\delta_0$</th>\n",
       "      <td>-1.3</td>\n",
       "      <td>-1.300000</td>\n",
       "      <td>2.220446e-16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\delta_1$</th>\n",
       "      <td>0.6</td>\n",
       "      <td>0.600000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\delta_2$</th>\n",
       "      <td>0.3</td>\n",
       "      <td>0.300000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              True value  Mean of estimates  SD of estimates\n",
       "$\\sigma_1^2$         1.0           1.944208     1.394589e+00\n",
       "$\\phi_{1,0}$         0.0           0.002687     7.451277e-02\n",
       "$\\phi_{1,1}$         0.6           0.666071     1.060599e-01\n",
       "$\\phi_{1,2}$        -0.2          -0.199086     4.947150e-02\n",
       "$\\sigma_2^2$         3.0           2.480053     7.875261e-01\n",
       "$\\phi_{2,0}$         0.0           0.004845     1.360822e-01\n",
       "$\\phi_{2,1}$         1.5           1.221861     3.929151e-01\n",
       "$\\delta_0$          -1.3          -1.300000     2.220446e-16\n",
       "$\\delta_1$           0.6           0.600000     0.000000e+00\n",
       "$\\delta_2$           0.3           0.300000     0.000000e+00"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "index = [r'$\\sigma_1^2$', r'$\\phi_{1,0}$', r'$\\phi_{1,1}$', \n",
    "         r'$\\phi_{1,2}$', r'$\\sigma_2^2$', r'$\\phi_{2,0}$', r'$\\phi_{2,1}$', r'$\\delta_0$', r'$\\delta_1$', \n",
    "         r'$\\delta_2$']\n",
    "columns = ['True value', 'Mean of estimates', 'SD of estimates']\n",
    "results_df = pd.DataFrame(index=index, columns=columns)\n",
    "results_df['True value'] = [1, 0, 0.6, -0.2, 3, 0, 1.5, -1.3, 0.6, 0.3]\n",
    "parameters = [var_1s, phi_10s, phi_11s, phi_12s, var_2s, phi_20s, phi_21s, \n",
    "              delta_0s, delta_1s, delta_2s]\n",
    "    \n",
    "results_df['Mean of estimates'] = [np.nanmean(remove_outliers(x)) for x in parameters]\n",
    "results_df['SD of estimates'] = [np.nanstd(remove_outliers(x)) for x in parameters]\n",
    "results_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6ee47eba",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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