Sample Code/Day_28_SampleCode.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 今天的範例，帶大家運用python 裡面的套件\n",
    "* 如何模擬這些分配的樣本點\n",
    "* 進行一些機率的運算\n",
    "\n",
    "包含以下離散型分配        \n",
    "\n",
    "\n",
    "4. 負二項分配(Negative Binomial Distribution)  \n",
    "5. 超幾何分配(Hypergeometric Distribution)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# library\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats\n",
    "import math\n",
    "import statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. 負二項分配(Negative Binomial Distribution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.  1.  2.  3.  4.  5.  6.  7.  8.  9. 10. 11. 12. 13. 14.]\n",
      "[0.064      0.1152     0.13824    0.13824    0.124416   0.10450944\n",
      " 0.08360755 0.06449725 0.04837294 0.03547349 0.02554091 0.01811083\n",
      " 0.01267758 0.00877679 0.00601837]\n",
      "<class 'numpy.ndarray'>\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''\n",
    "# 負二項分配(Negative Binomial Distribution)\n",
    "# 前提：在一系列獨立同分布的伯努利試驗中，X為成功次數到達指定次數（記為 𝑘 ）時，需要試驗的次數的機率分布\n",
    "p: 成功的機率\n",
    "k: 累積到 k 次成功後才停整\n",
    "r: 產生出 樣本點空間\n",
    "'''\n",
    "# 1.定義負二項分配的基本資訊\n",
    "p = 0.4 #成功的機率\n",
    "k = 3   #指定次數\n",
    "\n",
    "#產生一個同樣間隔的序列\n",
    "#print(stats.nbinom.ppf(0.01, k, p)) #0.0\n",
    "#print(stats.nbinom.ppf(0.99, k, p)) #15\n",
    "\n",
    "r = np.arange(stats.nbinom.ppf(0.01, k,p),\n",
    "              stats.nbinom.ppf(0.99, k,p))\n",
    "print(r)\n",
    "\n",
    "# 2.計算機率質量函數 (probability mass function)\n",
    "# P(X=x) --> 是機率\n",
    "probs = stats.nbinom.pmf(r,k,p)\n",
    "print(probs)\n",
    "print(type(probs))\n",
    "\n",
    "plt.bar(r, probs)\n",
    "plt.ylabel('P(X=x)')\n",
    "plt.xlabel('x')\n",
    "plt.title('NB(k=3,p=0.4)')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Eka1Zedz9xkL6tm3EfSP6BB1HRGoIFYI4UVTs3DVlPvsLi3nyykHqWlpEqoyu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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 3.計算負二項分佈的累積機率 (cumulative density function)，pmf 的累加\n",
    "# P(X=x) --> 是機率\n",
    "cumsum_probs = stats.nbinom.cdf(r, k, p)\n",
    "#array([ 0.07776, 0.2592 , 0.3456 , 0.2304 , 0.0768 , 0.01024])\n",
    "plt.show()\n",
    "plt.ylabel('P(X<=x)')\n",
    "plt.xlabel('x')\n",
    "plt.title('binomial(n=5,p=0.4)')\n",
    "plt.plot(r, cumsum_probs)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.  1.  2.  3.  4.  5.  6.  7.  8.  9. 10. 11. 12. 13. 14.]\n"
     ]
    }
   ],
   "source": [
    "# 4.透過 cdf ，給定一個 機率值，反推出對應到的 x\n",
    "p_loc= stats.nbinom.ppf(cumsum_probs, k, p)\n",
    "print(p_loc)\n",
    "#看上圖看結果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1  5  0  8  3 15  4 11  2  6  5  1 11  2  7 15  7  4  6 12]\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 5.產生符合負二項分佈的隨機樣本點 (random sample)\n",
    "X = stats.nbinom.rvs(k,p,size=20)\n",
    "print(X)\n",
    "plt.hist(X)\n",
    "plt.show()\n",
    "#試試看，，每一次的結果一樣嗎?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array(4.5), array(11.25), array(1.19256959), array(2.08888889))\n",
      "<class 'tuple'>\n",
      "negative binomial mean= 4.5\n",
      "negative binomial variance= 11.25\n",
      "negative binomial kurtosis= 1.1925695879998879\n",
      "negative binomial skew= 2.088888888888889\n"
     ]
    }
   ],
   "source": [
    "#6.計算固定參數下，隨機變數的平均數、變異數、偏度和峰度。\n",
    "stat_nbin=stats.nbinom.stats(k,p,moments='mvks')\n",
    "print(stat_nbin)\n",
    "print(type(stat_nbin))\n",
    "#E(X)\n",
    "print(\"negative binomial mean=\",float(stat_nbin[0]))\n",
    "print(\"negative binomial variance=\",float(stat_nbin[1]))\n",
    "print(\"negative binomial kurtosis=\",float(stat_nbin[2]))\n",
    "print(\"negative binomial skew=\",float(stat_nbin[3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. 超幾何分配(Hypergeometric Distribution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  1  2  3  4  5  6  7  8  9 10]\n",
      "[1.79858837e-05 4.90524100e-04 5.33444958e-03 3.06388899e-02\n",
      " 1.03406253e-01 2.15085007e-01 2.80058603e-01 2.25929629e-01\n",
      " 1.08257947e-01 2.78558461e-02 2.92486384e-03]\n",
      "<class 'numpy.ndarray'>\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''\n",
    "超幾何分配(Hypergeometric Distribution)描述了\n",
    "由有限個物件中抽出n個物件，成功抽出指定種類的物件的個數（不歸還 （without replacement）)\n",
    "若隨機變量X 服從參數，則記為  H(n,K,N)，\n",
    "𝑁 : 共有幾個物件, 𝑁 =0,1,…\n",
    "𝐾 : 𝑁 個物件中，有 𝐾 個是你關心的物件類型個數, 𝐾 =0,1,2,…, 𝑁\n",
    "𝑛 : K個物件，要抽出 𝑛 個物件, 𝑛 =0,1,…, 𝑁\n",
    "\n",
    "現在有兩堆骰子，30個為紅色數字，20個為黑色數字，取出10個，X=有幾個是紅色的。\n",
    "'''\n",
    "# 1.定義超幾何分配的基本資訊\n",
    "N=50\n",
    "K=30\n",
    "n=10\n",
    "\n",
    "#產生一個同樣間隔的序列\n",
    "r = np.arange(0, min(n+1,K+1)) #產出 x 對應點\n",
    "print(r)\n",
    "\n",
    "# 2.計算機率質量函數 (probability mass function)\n",
    "# P(X=x) --> 是機率\n",
    "probs = stats.hypergeom.pmf(r, N,K,n)\n",
    "print(probs)\n",
    "print(type(probs))\n",
    "\n",
    "plt.bar(r, probs)\n",
    "plt.ylabel('P(X=x)')\n",
    "plt.xlabel('x')\n",
    "plt.title('pmf of Hypergeometric(N=50,K=30,n=10)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NOBY4uKoNmdnlwOUA3bp1q2oxkXrlzldmkJuTzVUah1jquerUCEoqnlSnSShB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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 3.計算超幾何分配的累積機率 (cumulative density function)，pmf 的累加\n",
    "# P(X=x) --> 是機率\n",
    "cumsum_probs = stats.hypergeom.cdf(r, N,K,n)\n",
    "plt.show()\n",
    "plt.ylabel('P(X<=x)')\n",
    "plt.xlabel('x')\n",
    "plt.title('cdf of Hypergeometric(N=50,K=30,n=10)')\n",
    "plt.plot(r, cumsum_probs)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.  1.  2.  3.  4.  5.  6.  7.  8.  9. 10.]\n"
     ]
    }
   ],
   "source": [
    "# 4.透過 cdf ，給定一個 機率值，反推出對應到的 x\n",
    "p_loc= stats.hypergeom.ppf(cumsum_probs, N,K,n)\n",
    "print(p_loc)\n",
    "#看上圖看結果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[7 5 8 8 7 4 9 8 8 6 6 8 7 8 7 6 6 9 6 5]\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWoAAAD4CAYAAADFAawfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhBoAiiPUAFAcoQaA4gg1ABT3fw6Je2azV8QcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 5.產生符合超幾何分配的隨機樣本點 (random sample)\n",
    "X = stats.hypergeom.rvs(N,K,n,size=20)\n",
    "print(X)\n",
    "plt.hist(X,bins=25)\n",
    "plt.show()\n",
    "#試試看，，每一次的結果一樣嗎?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array(6.), array(1.95918367), array(-0.08930431), array(-0.13162123))\n",
      "<class 'tuple'>\n",
      "negative hypergeom mean= 6.0\n",
      "negative hypergeom variance= 1.9591836734693877\n",
      "negative hypergeom kurtosis= -0.08930431353897003\n",
      "negative hypergeom skew= -0.13162123226950354\n"
     ]
    }
   ],
   "source": [
    "#6.計算固定參數下，隨機變數的平均數、變異數、偏度和峰度。\n",
    "\n",
    "stat_hyperg=stats.hypergeom.stats(N,K,n,moments='mvks')\n",
    "print(stat_hyperg)\n",
    "print(type(stat_hyperg))\n",
    "#E(X)\n",
    "print(\"negative hypergeom mean=\",float(stat_hyperg[0]))\n",
    "print(\"negative hypergeom variance=\",float(stat_hyperg[1]))\n",
    "print(\"negative hypergeom kurtosis=\",float(stat_hyperg[2]))\n",
    "print(\"negative hypergeom skew=\",float(stat_hyperg[3]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### #投影片例子: 丟 5次骰子出現紅色三次的機率\n",
    "![](Binomail_example.PNG)\n",
    "![](data.PNG)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](data.PNG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1646090534979424\n",
      "0.16460905349794233\n"
     ]
    }
   ],
   "source": [
    "# 用 python 計算\n",
    "# 直接公式是運算\n",
    "n=5\n",
    "p=1/3\n",
    "prob1=math.factorial(5)/math.factorial(2)/math.factorial(3)*pow(p,3)*pow((1-p),2) #page\n",
    "print(prob1)\n",
    "\n",
    "#P(X=3)\n",
    "probs = stats.binom.pmf(3, n, p)\n",
    "print(probs)\n",
    "#兩者是相同的"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "name": "Day33.YOLO 細節理解 - 網路輸出的後處理_HW.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}