Lec091.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 連続一様分布について解説します。離散一様分布を先に見ておいてください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "離散一様分布では、取り得る値と確率を分かりやすく対応付けることができました。しかし、連続一様分布ではそうは行きません。無限の精度を求めると、いくらでも数字を細かくできます。これは、2つの数字を考えたとき、その間から必ず別の数字を選べるという意味でもあります。例えば、5.41と5.42を考えると、5.415を選べます。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "そう考えると、連続一様分布では、取り得る値の個数nが無限大になります。そうなると、確率は1/∞になってしまうので、0です。これでは話が始まりませんので、連続分布で確率を考えるときは、1点ではなく、領域を考えます。これを分かり易くするために、例を交えながら、さらに見ていくことにしましょう。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 連続な確率変数Xが次のような確率密度関数（probability density function）に従うとき、これを連続一様分布と呼びます。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$f(x)=\\frac{1}{(b-a)}\\\\\\\\a<=x<=b$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "離散一様分布では、f(x)=1/n でしたが、連続一様分布では、最小値aと最大値bの間で定義される領域を考えます。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "分布の平均は単純です。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac{(a+b)}{2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "分散は次のように定義されます。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\sigma^2 = \\frac{(b-a)^2}{12}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ニューヨーク市での平均的なタクシーの乗車時間は22分くらいであることが知られています。調査の結果、この乗車時間が、19分から27分の間の連続的な一様分布に従うことが分かったとします。タクシー乗車時間の確率密度関数を求めてみましょう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "確率密度関数は、0.125\n"
     ]
    }
   ],
   "source": [
    "# 乗車時間の下限\n",
    "a = 19\n",
    "\n",
    "# 上限\n",
    "b = 27\n",
    "\n",
    "# 連続一様分布の確率密度関数です。\n",
    "fx = 1.0/(b-a)\n",
    "\n",
    "print(f'確率密度関数は、{fx}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "分散=5.333333333333333\n"
     ]
    }
   ],
   "source": [
    "# 分散\n",
    "var = ((b-a)**2 )/12\n",
    "\n",
    "print(f'分散={var}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "乗車時間が少なくとも25分続く確率を計算してみましょう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "乗車時間が少なくとも25分かかる確率は25.0%\n"
     ]
    }
   ],
   "source": [
    "# これは、全体から、乗車時間が25分より短い場合を引けばよいので、次のようにして求めることができます。\n",
    "\n",
    "# 乗車時間が27分までに収まる確率は全体なので1です。\n",
    "# 一方、乗車時間が25分までに収まる確率は、\n",
    "f25 = (25-19)/(b-a)\n",
    "\n",
    "ans = 1-f25\n",
    "\n",
    "print(f'乗車時間が少なくとも25分かかる確率は{100*ans}%')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "scipyを使って便利に連続一様分布を作ってみます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12fa0b850>]"
      ]
     },
     "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": [
    "from scipy.stats import uniform\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 最小と最大を作ります。\n",
    "A=0\n",
    "B=5\n",
    "\n",
    "# AからBまで100ポイントを作っておきます。\n",
    "x = np.linspace(A, B, 100)\n",
    "\n",
    "# 連続一様分布は、uniform(loc=start point,scale=endpoint)で作れます。\n",
    "rv = uniform(loc=A, scale=B)\n",
    "\n",
    "# 確率密度関数（PDF）と累積分布関数（Cumulative Distribution Function)を描いてみます。\n",
    "plt.plot(x, rv.pdf(x))\n",
    "plt.plot(x, rv.cdf(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "青い線は、0.2のところにありますが、1/(5-0) が 1/5 で 0.2なので、すぐに確かめられます。\n",
    "\n",
    "#### 2,3は英語ですが、Web上にも有用な情報があります。\n",
    "\n",
    "1.)https://ja.wikipedia.org/wiki/%E9%80%A3%E7%B6%9A%E4%B8%80%E6%A7%98%E5%88%86%E5%B8%83\n",
    "\n",
    "2.)http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.uniform.html\n",
    "\n",
    "3.)http://mathworld.wolfram.com/UniformDistribution.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
}