lab2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "start_time": "2023-04-05T09:25:29.177055Z",
     "end_time": "2023-04-05T09:25:29.955036Z"
    }
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import abc\n",
    "from typing import Callable\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats\n",
    "%matplotlib inline\n",
    "\n",
    "np.random.seed(int.from_bytes(os.urandom(4), byteorder=\"big\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [],
   "source": [
    "class PoissonProcess(abc.ABC):\n",
    "    @abc.abstractmethod\n",
    "    def generate(self, t: float) -> float:\n",
    "        pass\n",
    "\n",
    "    @abc.abstractmethod\n",
    "    def generate_series(self, t: float) -> pd.Series:\n",
    "        pass"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2023-04-05T09:25:29.957664Z",
     "end_time": "2023-04-05T09:25:29.960336Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [],
   "source": [
    "class HomogenousPoissonProcess(PoissonProcess):\n",
    "    def __init__(self, lambda_: float):\n",
    "        self.lambda_: float = lambda_\n",
    "\n",
    "    def generate(self, t: float) -> float:\n",
    "        u = np.random.uniform()\n",
    "        t = t - 1 / self.lambda_ * np.log(u)\n",
    "        return t\n",
    "\n",
    "    def generate_series(self, t: float) -> pd.Series:\n",
    "        t_ = 0\n",
    "        s = []\n",
    "        while True:\n",
    "            t_ = self.generate(t_)\n",
    "            if t_ > t:\n",
    "                break\n",
    "            s.append(t_)\n",
    "        s = pd.Series(s)\n",
    "        return s"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2023-04-05T09:25:29.963502Z",
     "end_time": "2023-04-05T09:25:29.982681Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [],
   "source": [
    "class InhomogeneousPoissonProcess(PoissonProcess):\n",
    "    def __init__(self, lambda_: float, lambda_t: Callable[[float], float]):\n",
    "        self.lambda_: float = lambda_\n",
    "        self.lambda_t: Callable[[float], float] = lambda_t\n",
    "\n",
    "    def generate(self, t: float) -> float:\n",
    "        while True:\n",
    "            u1 = np.random.uniform()\n",
    "            t = t - 1 / self.lambda_ * np.log(u1)\n",
    "            u2 = np.random.uniform()\n",
    "            if u2 <= self.lambda_t(t) / self.lambda_:\n",
    "                return t\n",
    "\n",
    "    def generate_series(self, t: float) -> pd.Series:\n",
    "        t_ = 0\n",
    "        s = []\n",
    "        while True:\n",
    "            t_ = self.generate(t_)\n",
    "            if t_ > t:\n",
    "                break\n",
    "            s.append(t_)\n",
    "        s = pd.Series(s)\n",
    "        return s"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2023-04-05T09:25:29.979131Z",
     "end_time": "2023-04-05T09:25:29.983886Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "outputs": [],
   "source": [
    "@np.vectorize\n",
    "def exp_prob(lambda_: float, start: float, end: float) -> float:\n",
    "    return np.exp(-lambda_ * start) - np.exp(-lambda_ * end)\n",
    "\n",
    "def chi2_exp(bins: np.ndarray, counts: np.ndarray) -> tuple[float, int, pd.DataFrame]:\n",
    "    n = int(np.sum(counts))\n",
    "    values = (bins[1:] + bins[:-1]) / 2\n",
    "    x_b = np.sum(values * counts) / n\n",
    "    lambda_s = 1 / x_b\n",
    "    p = exp_prob(lambda_s, bins[:-1], bins[1:])\n",
    "    ni = p * n\n",
    "    delta_n = counts - ni\n",
    "    delta_n2 = delta_n ** 2\n",
    "    k = delta_n2 / ni\n",
    "    table = pd.DataFrame({\"i\": values, \"n_i\": counts, \"n'_i\": ni, \"n_i - n'_i\": delta_n, \"(n_i - n'_i)^2\": delta_n2, \"K\": k}).set_index('i', drop=True)\n",
    "    df = len(values) - 2\n",
    "    return float(np.sum(k)), df, table\n",
    "\n",
    "def chi2_test(pp: PoissonProcess, alpha: float, t: float):\n",
    "    inc = pp.generate_series(t)\n",
    "    display(inc)\n",
    "    inc = inc.to_numpy()\n",
    "    intervals = inc[1:] - inc[:-1]\n",
    "\n",
    "    b = np.linspace(np.floor(intervals.min()), np.ceil(intervals.max()), int(1 + np.log2(len(intervals))))\n",
    "    c, _ = np.histogram(intervals, bins=b)\n",
    "\n",
    "    plt.stairs(c, b)\n",
    "\n",
    "    chi2, df, t = chi2_exp(b.copy(), c.copy())\n",
    "\n",
    "    chi2_crit = scipy.stats.chi2.isf(alpha, df=df, loc=0, scale=1)\n",
    "\n",
    "    dft = pd.DataFrame.from_dict({\n",
    "        \"df\": df,\n",
    "        \"chi2\": chi2,\n",
    "        \"chi2_crit\": chi2_crit,\n",
    "        \"H0\": \"принимаем\" if chi2 < chi2_crit else \"отвергаем\"\n",
    "    }, orient=\"index\")\n",
    "    display(dft)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2023-04-05T09:32:03.111820Z",
     "end_time": "2023-04-05T09:32:03.155367Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "outputs": [],
   "source": [
    "T = 100\n",
    "POISSON_LAMBDA = 2\n",
    "POISSON_LAMBDA_T = lambda t: 1 + 1 / np.sqrt(t)\n",
    "ALPHA = 0.05"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2023-04-05T09:32:03.914183Z",
     "end_time": "2023-04-05T09:32:03.922185Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "outputs": [],
   "source": [
    "hpp = HomogenousPoissonProcess(POISSON_LAMBDA)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2023-04-05T09:32:04.448583Z",
     "end_time": "2023-04-05T09:32:04.456776Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "outputs": [
    {
     "data": {
      "text/plain": "0       0.384767\n1       1.292787\n2       1.847854\n3       2.490376\n4       3.515651\n         ...    \n172    97.119428\n173    97.315324\n174    98.089496\n175    98.526341\n176    98.809276\nLength: 177, dtype: float64"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "                   0\ndf                 5\nchi2        6.774672\nchi2_crit  11.070498\nH0         принимаем",
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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HTp8+HXv37o22trY4evRoRLx6JWXevHnFNd3d3SOuqpxRXl4e5eXlpR4VAEhUya+grFixIn7605/G4cOHi4/FixfHnXfeGYcPH45rrrkmqquro729vfiaoaGh6OjoiGXLlpV6HABgHCr5FZTKyspYuHDhsGPTp0+POXPmFI83NjZGc3Nz1NXVRV1dXTQ3N8e0adNi1apVpR4HABiHxuQm2XNZv359nDp1KtauXRs9PT2xZMmS2LNnT1RWVuYxDgCQmIsSKE888cSwrwuFQjQ1NUVTU9PF+OcBgHHG3+IBAJIjUACA5AgUACA5AgUASI5AAQCSI1AAgOQIFAAgOQIFAEiOQAEAkiNQAIDk5PK3eEjfs90n8h4hV7Onl8X8WRV5jwEwYQkUhpk9vSwqpkyKxl2H8x4lVxVTJsVj99aLFICcCBSGmT+rIh67tz56BobyHiU3z3afiMZdh6NnYEigAOREoDDC/FkVvjEDkCs3yQIAyREoAEByBAoAkByBAgAkR6AAAMkRKABAcgQKAJAcgQIAJEegAADJESgAQHIECgCQHIECACRHoAAAyREoAEByBAoAkByBAgAkR6AAAMkRKABAcgQKAJAcgQIAJEegAADJESgAQHIECgCQHIECACRHoAAAyREoAEByBAoAkByBAgAkR6AAAMkRKABAcgQKAJAcgQIAJEegAADJESgAQHIECgCQHIECACRHoAAAyREoAEByBAoAkByBAgAkZ3LeA0Cqnu0+kfcIuZk9vSzmz6rIewxgAhMocJbZ08uiYsqkaNx1OO9RclMxZVI8dm+9SAFyI1DgLPNnVcRj99ZHz8BQ3qPk4tnuE9G463D0DAwJFCA3AgVGMX9WhW/OADlykywAkByBAgAkR6AAAMkRKABAckoeKC0tLXHjjTdGZWVlzJ07N2677bY4evTosDVZlkVTU1PU1NRERUVFLF++PI4cOVLqUQCAcarkgdLR0RF33313/PjHP4729vZ4+eWXo6GhIQYGBoprtmzZElu3bo22trbYv39/VFdXx8qVK6O/v7/U4wAA41DJf834n//5n4d9/eCDD8bcuXPj4MGD8f73vz+yLIvW1tbYtGlT3H777RERsWPHjqiqqoqdO3fGmjVrSj0SADDOjPk9KL29vRERcfnll0dExLFjx6KrqysaGhqKa8rLy6O+vj727ds36nsMDg5GX1/fsAcAcOka00DJsizWrVsXN910UyxcuDAiIrq6uiIioqqqatjaqqqq4nNna2lpiZkzZxYfCxYsGMuxAYCcjWmg3HPPPfHUU0/Fd7/73RHPFQqFYV9nWTbi2BkbN26M3t7e4qOzs3NM5gUA0jBmH3X/qU99Kh599NHYu3dvXHnllcXj1dXVEfHqlZR58+YVj3d3d4+4qnJGeXl5lJeXj9WoAEBiSn4FJcuyuOeee+KRRx6JH/zgB1FbWzvs+dra2qiuro729vbisaGhoejo6Ihly5aVehwAYBwq+RWUu+++O3bu3Bn/+I//GJWVlcX7SmbOnBkVFRVRKBSisbExmpubo66uLurq6qK5uTmmTZsWq1atKvU4AMA4VPJA2bZtW0RELF++fNjxBx98MP7oj/4oIiLWr18fp06dirVr10ZPT08sWbIk9uzZE5WVlaUeBwAYh0oeKFmWnXNNoVCIpqamaGpqKvU/DwBcAvwtHgAgOQIFAEiOQAEAkiNQAIDkCBQAIDkCBQBIjkABAJIjUACA5AgUACA5AgUASI5AAQCSI1AAgOQIFAAgOQIFAEiOQAEAkiNQAIDkCBQAIDkCBQBIjkABAJIjUACA5AgUACA5AgUASI5AAQCSI1AAgOQIFAAgOQIFAEiOQAEAkiNQAIDkTM57ACBNz3afyHuEXM2eXhbzZ1XkPQZMWAIFGGb29LKomDIpGncdznuUXFVMmRSP3VsvUiAnAgUYZv6sinjs3vroGRjKe5TcPNt9Ihp3HY6egSGBAjkRKMAI82dV+MYM5EqgALyGiXwfjntwyJtAATiL+3Dcg0P+BArAWSb6fTjuwSEFAgVgFO7DgXz5oDYAIDkCBQBIjkABAJIjUACA5AgUACA5AgUASI5AAQCSI1AAgOQIFAAgOQIFAEiOQAEAkiNQAIDkCBQAIDkCBQBIjkABAJIjUACA5AgUACA5AgUASI5AAQCSI1AAgOQIFAAgOZPzHgCAND3bfSLvEXIze3pZzJ9VkfcYE5pAAWCY2dPLomLKpGjcdTjvUXJTMWVSPHZvvUjJkUABYJj5syrisXvro2dgKO9RcvFs94lo3HU4egaGBEqOBAoAI8yfVeGbM7nK9SbZBx54IGpra2Pq1KmxaNGi+OEPf5jnOABAInILlF27dkVjY2Ns2rQpDh06FDfffHN88IMfjBdeeCGvkQCAROQWKFu3bo1PfvKT8cd//Mfx9re/PVpbW2PBggWxbdu2vEYCABKRyz0oQ0NDcfDgwdiwYcOw4w0NDbFv374R6wcHB2NwcLD4dW9vb0RE9PX1lXy2E/198crgyTjR3xd9fYWSvz8AaTvzfeCp547Hif7Sf58ZL654U3lcMWNqSd/zzPftLMvOuTaXQHnxxRfj9OnTUVVVNex4VVVVdHV1jVjf0tISmzdvHnF8wYIFYzbj0tYxe2sAxoE7W/Oe4NLV398fM2fOfN01uf4WT6Ew/ApFlmUjjkVEbNy4MdatW1f8+pVXXon//d//jTlz5oy6/tfR19cXCxYsiM7OzpgxY0ZJ3/tS41ydP+fq/DlX58+5ujDO1/kbq3OVZVn09/dHTU3NOdfmEihvfvObY9KkSSOulnR3d4+4qhIRUV5eHuXl5cOOzZo1ayxHjBkzZtjA58m5On/O1flzrs6fc3VhnK/zNxbn6lxXTs7I5SbZsrKyWLRoUbS3tw873t7eHsuWLctjJAAgIbn9iGfdunXx8Y9/PBYvXhxLly6N7du3xwsvvBB33XVXXiMBAInILVDuuOOO+J//+Z+477774vjx47Fw4cL43ve+F1dddVVeI0XEqz9O+qu/+qsRP1JiJOfq/DlX58+5On/O1YVxvs5fCueqkJ3P7/oAAFxEuX7UPQDAaAQKAJAcgQIAJEegAADJmZCB8sADD0RtbW1MnTo1Fi1aFD/84Q9fd31HR0csWrQopk6dGtdcc018/etfv0iT5u9CztUTTzwRhUJhxOM///M/L+LE+di7d2985CMfiZqamigUCvEP//AP53zNRN1XF3quJuq+amlpiRtvvDEqKytj7ty5cdttt8XRo0fP+bqJuq/eyPmaqHtr27Zt8e53v7v4IWxLly6N73//+6/7mjz21YQLlF27dkVjY2Ns2rQpDh06FDfffHN88IMfjBdeeGHU9ceOHYsPfehDcfPNN8ehQ4fi85//fHz605+Ohx9++CJPfvFd6Lk64+jRo3H8+PHio66u7iJNnJ+BgYG4/vrro62t7bzWT+R9daHn6oyJtq86Ojri7rvvjh//+MfR3t4eL7/8cjQ0NMTAwMBrvmYi76s3cr7OmGh768orr4y//uu/jgMHDsSBAwfit3/7t+OjH/1oHDlyZNT1ue2rbIL5zd/8zeyuu+4aduy6667LNmzYMOr69evXZ9ddd92wY2vWrMne+973jtmMqbjQc/X4449nEZH19PRchOnSFRHZ7t27X3fNRN5X/9f5nCv76lXd3d1ZRGQdHR2vuca++pXzOV/21q/Mnj07+9u//dtRn8trX02oKyhDQ0Nx8ODBaGhoGHa8oaEh9u3bN+prfvSjH41Y/4EPfCAOHDgQL7300pjNmrc3cq7OuOGGG2LevHmxYsWKePzxx8dyzHFrou6rX8dE31e9vb0REXH55Ze/5hr76lfO53ydMZH31unTp+Ohhx6KgYGBWLp06ahr8tpXEypQXnzxxTh9+vSIP0hYVVU14g8XntHV1TXq+pdffjlefPHFMZs1b2/kXM2bNy+2b98eDz/8cDzyyCNx7bXXxooVK2Lv3r0XY+RxZaLuqzfCvnr1L8CuW7cubrrppli4cOFrrrOvXnW+52si762f/vSn8aY3vSnKy8vjrrvuit27d8c73vGOUdfmta9y+6j7PBUKhWFfZ1k24ti51o92/FJ0Iefq2muvjWuvvbb49dKlS6OzszO+9KUvxfvf//4xnXM8msj76kLYVxH33HNPPPXUU/Hkk0+ec619df7nayLvrWuvvTYOHz4cv/zlL+Phhx+O1atXR0dHx2tGSh77akJdQXnzm98ckyZNGnEFoLu7e0QdnlFdXT3q+smTJ8ecOXPGbNa8vZFzNZr3vve98V//9V+lHm/cm6j7qlQm0r761Kc+FY8++mg8/vjjceWVV77uWvvqws7XaCbK3iorK4u3ve1tsXjx4mhpaYnrr78+/uZv/mbUtXntqwkVKGVlZbFo0aJob28fdry9vT2WLVs26muWLl06Yv2ePXti8eLFMWXKlDGbNW9v5FyN5tChQzFv3rxSjzfuTdR9VSoTYV9lWRb33HNPPPLII/GDH/wgamtrz/maibyv3sj5Gs1E2FujybIsBgcHR30ut301prfgJuihhx7KpkyZkn3zm9/Mnn766ayxsTGbPn169t///d9ZlmXZhg0bso9//OPF9c8991w2bdq07DOf+Uz29NNPZ9/85jezKVOmZH//93+f13/CRXOh5+orX/lKtnv37uyZZ57Jfvazn2UbNmzIIiJ7+OGH8/pPuGj6+/uzQ4cOZYcOHcoiItu6dWt26NCh7Pnnn8+yzL76vy70XE3UffUnf/In2cyZM7MnnngiO378ePFx8uTJ4hr76lfeyPmaqHtr48aN2d69e7Njx45lTz31VPb5z38+u+yyy7I9e/ZkWZbOvppwgZJlWfa1r30tu+qqq7KysrLsN37jN4b9Gtrq1auz+vr6YeufeOKJ7IYbbsjKysqyq6++Otu2bdtFnjg/F3Ku7r///uytb31rNnXq1Gz27NnZTTfdlP3TP/1TDlNffGd+XfHsx+rVq7Mss6/+rws9VxN1X412jiIie/DBB4tr7KtfeSPna6LurU984hPF/1+/4oorshUrVhTjJMvS2VeFLPv/d7oAACRiQt2DAgCMDwIFAEiOQAEAkiNQAIDkCBQAIDkCBQBIjkABAJIjUACA5AgUACA5AgUASI5AAQCSI1AAgOT8Px9k/GNh48xMAAAAAElFTkSuQmCC\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "chi2_test(hpp, ALPHA, T)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2023-04-05T09:32:04.961533Z",
     "end_time": "2023-04-05T09:32:05.157683Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "outputs": [],
   "source": [
    "ipp = InhomogeneousPoissonProcess(POISSON_LAMBDA, POISSON_LAMBDA_T)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2023-04-05T09:30:35.489498Z",
     "end_time": "2023-04-05T09:30:35.531127Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "outputs": [
    {
     "data": {
      "text/plain": "0     0.473240\n1     1.512422\n2     2.724584\n3     3.761417\n4     4.403459\n5     5.417829\n6     6.471744\n7     7.490457\n8     9.148791\n9     9.222852\n10    9.357586\ndtype: float64"
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ipp.generate_series(10)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2023-04-05T09:30:42.350066Z",
     "end_time": "2023-04-05T09:30:42.355205Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2023-04-05T09:30:37.254971Z",
     "end_time": "2023-04-05T09:30:37.295653Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
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