Lec093.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### ポアソン分布とは？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ポアソン分布は、ある間隔（時間や長さなど）の間に起こるイベントの回数に注目するものです。\n",
    "まずは、その定義をみたあとに、その式の意味するところを噛み砕いていくことにしましょう。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "離散確率変数Xが、パラメータλを持つポアソン分布に従うとき、k=0,1,2.., に対応する確率を生成する確率質量関数は、次の式で与えられます。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$Pr(X=k)=\\frac{\\lambda^ke^{-\\lambda}}{k!}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "eは自然対数の底（ネイピア数）で、e=2.718...となる数です。k!はkの階乗。      "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ポアソン分布には、次のような性質があります。\n",
    "\n",
    "    1. 離散的です。(x=0,1,2,3...)\n",
    "    1. この数は、0から無限大までの値を取り得ます。\n",
    "    1. あまり頻繁には起こらない事象の確率分布を表現します。\n",
    "    1. それぞれの事象は独立です。\n",
    "    1. 時間や距離などの間隔で起きる事象について記述します。\n",
    "    1. 事象が起きる回数の期待値は定数です。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "例を見てみましょう。\n",
    "\n",
    "マクドナルドのランチのピークは、12:30から1:00の間です。これまでの経験から、平均で10人のお客さんが、この時間帯に来店することが分かっています。それでは、ちょうど7人のお客さんが来店する確率はどれくらいでしょうか？また、10人より多いお客さんが来る確率はどれくらいでしょうか？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "これまでの経験から、お昼のピーク30分間に、10人のお客さんが来ることがわかっています。この10は平均値、つまり期待値です。これはポアソン分布のパラメータλに相当します。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ポアソン分布はλが決まれば、決まりますので、この例題に答えることができます。やってみましょう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "昼のピーク時にお客さんが7人である確率は、9.01%です。\n"
     ]
    }
   ],
   "source": [
    "# 残念ながら、lambdaはPythonでは予約語なので、そのまま変数名には使えます。\n",
    "\n",
    "# lambとして、λをセットします。\n",
    "lamb = 10\n",
    "\n",
    "# ちょうど7人来る確率を計算したいので、k=7です。\n",
    "k=7\n",
    "\n",
    "# 標準mathモジュールから、必要なモノをインポート\n",
    "from math import exp\n",
    "from math import factorial\n",
    "\n",
    "# 確率質量関数をつかって確率を計算します。\n",
    "prob = (lamb**k)*exp(-lamb)/factorial(k)\n",
    "\n",
    "print(f'昼のピーク時にお客さんが7人である確率は、{100*prob:0.2f}%です。')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "確率質量関数を手作りできました。scipyを使うともう少し楽です。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ピーク時に7人の確率は9.01％\n",
      "平均=10.0\n"
     ]
    }
   ],
   "source": [
    "# scipy.statsから、 poissonをインポートします\n",
    "from scipy.stats import poisson\n",
    "\n",
    "# 平均は10です。\n",
    "mu = 10\n",
    "\n",
    "# 平均と分散を計算できます。\n",
    "mean, var = poisson.stats(mu)\n",
    "\n",
    "# 確率質量関数を使って、特定の確率を計算することも可能です。\n",
    "odds_seven = poisson.pmf(7, mu)\n",
    "\n",
    "print(f'ピーク時に7人の確率は{odds_seven*100:0.2f}％')\n",
    "\n",
    "print(f'平均={mean}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "分布の全体を見ておくことにします。これは、10人よりお客が多い確率を求めるのに必要です。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.53999298e-05, 4.53999298e-04, 2.26999649e-03, 7.56665496e-03,\n",
       "       1.89166374e-02, 3.78332748e-02, 6.30554580e-02, 9.00792257e-02,\n",
       "       1.12599032e-01, 1.25110036e-01, 1.25110036e-01, 1.13736396e-01,\n",
       "       9.47803301e-02, 7.29079462e-02, 5.20771044e-02, 3.47180696e-02,\n",
       "       2.16987935e-02, 1.27639962e-02, 7.09110899e-03, 3.73216263e-03,\n",
       "       1.86608131e-03, 8.88610150e-04, 4.03913704e-04, 1.75614654e-04,\n",
       "       7.31727725e-05, 2.92691090e-05, 1.12573496e-05, 4.16938875e-06,\n",
       "       1.48906741e-06, 5.13471521e-07])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 確率質量関数をプロットしてみましょう。\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "# ひとまず、30人のお客さんが来る確率です。理論的には無限大まであり得ます。\n",
    "k=np.arange(30)\n",
    "\n",
    "# 平均は10です。\n",
    "lamb = 10\n",
    "\n",
    "# これで確率を計算できます。\n",
    "pmf_pois = poisson.pmf(k, lamb)\n",
    "pmf_pois"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 30 artists>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "plt.bar(k, pmf_pois)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "10人より多くのお客さんがくる確率はどれくらいでしょうか？\n",
    "\n",
    "これは、11人以降の確率の値をすべて足し合わせれば良いわけですが、これを実現するのが、累積分布関数（CDF: Cumulative Distribution Function）です。\n",
    "\n",
    "累積分布関数は、指定された値までの確率を足し合わせた値を返してくれます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "お客さんが10人までの確率は、58.30%です。\n"
     ]
    }
   ],
   "source": [
    "# お客さんが10人までの確率を計算するので、k = 10です。平均値もおなじく10\n",
    "k, mu = 10, 10\n",
    "\n",
    "# お客さんが10人までの確率を次のコードで計算できます。\n",
    "prob_up_to_ten = poisson.cdf(k, mu)\n",
    "\n",
    "print(f'お客さんが10人までの確率は、{100*prob_up_to_ten:0.2f}%です。')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "10により多く来る確率は、1からこの値を引くだけです。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10人より多くのお客さんが来る確率は、41.70%です。\n"
     ]
    }
   ],
   "source": [
    "prob_more_than_ten = 1 - prob_up_to_ten\n",
    "\n",
    "print(f'10人より多くのお客さんが来る確率は、{100*prob_more_than_ten:0.2f}%です。')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ポアソン分布の基本的なことを解説しました。\n",
    "以下の資料も参考にしてみてください。\n",
    "\n",
    "1. https://ja.wikipedia.org/wiki/%E3%83%9D%E3%82%A2%E3%82%BD%E3%83%B3%E5%88%86%E5%B8%83\n",
    "\n",
    "1. https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.poisson.html"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}