{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 概率统计方法"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 简介"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**`Python`** 中常用的统计工具有 **`Numpy, Pandas, PyMC, StatsModels`** 等。\n",
    "\n",
    "**`Scipy`** 中的子库 `scipy.stats` 中包含很多统计上的方法。\n",
    "\n",
    "导入 `numpy` 和 `matplotlib`："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "heights = array([1.46, 1.79, 2.01, 1.75, 1.56, 1.69, 1.88, 1.76, 1.88, 1.78])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Numpy` 自带简单的统计方法："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean,  1.756\n",
      "min,  1.46\n",
      "max,  2.01\n",
      "standard deviation,  0.150811140172\n"
     ]
    }
   ],
   "source": [
    "print 'mean, ', heights.mean()\n",
    "print 'min, ', heights.min()\n",
    "print 'max, ', heights.max()\n",
    "print 'standard deviation, ', heights.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "导入 **`Scipy`** 的统计模块："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy.stats.stats as st"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "其他统计量："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "median,  1.77\n",
      "mode,  (array([ 1.88]), array([ 2.]))\n",
      "skewness,  -0.393524456473\n",
      "kurtosis,  -0.330672097724\n",
      "and so many more...\n"
     ]
    }
   ],
   "source": [
    "print 'median, ', st.nanmedian(heights)    # 忽略nan值之后的中位数\n",
    "print 'mode, ', st.mode(heights)           # 众数及其出现次数\n",
    "print 'skewness, ', st.skew(heights)       # 偏度\n",
    "print 'kurtosis, ', st.kurtosis(heights)   # 峰度\n",
    "print 'and so many more...'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 概率分布"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "常见的[连续概率分布](https://zh.wikipedia.org/wiki/Category:%E8%BF%9E%E7%BB%AD%E5%88%86%E5%B8%83)有：\n",
    "\n",
    "- 均匀分布\n",
    "- 正态分布\n",
    "- 学生`t`分布\n",
    "- `F`分布\n",
    "- `Gamma`分布\n",
    "- ...\n",
    "\n",
    "[离散概率分布](https://zh.wikipedia.org/wiki/Category:%E7%A6%BB%E6%95%A3%E5%88%86%E5%B8%83)：\n",
    "\n",
    "- 伯努利分布\n",
    "- 几何分布\n",
    "- ...\n",
    "\n",
    "这些都可以在 `scipy.stats` 中找到。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 连续分布"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 正态分布"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以[正态分布](https://zh.wikipedia.org/wiki/%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83)为例，先导入正态分布："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "它包含四类常用的函数：\n",
    "\n",
    "- `norm.cdf` 返回对应的[累计分布函数](https://zh.wikipedia.org/wiki/%E7%B4%AF%E7%A7%AF%E5%88%86%E5%B8%83%E5%87%BD%E6%95%B0)值\n",
    "- `norm.pdf` 返回对应的[概率密度函数](https://zh.wikipedia.org/wiki/%E6%A9%9F%E7%8E%87%E5%AF%86%E5%BA%A6%E5%87%BD%E6%95%B8)值\n",
    "- `norm.rvs` 产生指定参数的随机变量\n",
    "- `norm.fit` 返回给定数据下，各参数的[最大似然估计](https://zh.wikipedia.org/wiki/%E6%9C%80%E5%A4%A7%E4%BC%BC%E7%84%B6%E4%BC%B0%E8%AE%A1)（MLE）值\n",
    "\n",
    "从正态分布产生500个随机点："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_norm = norm.rvs(size=500)\n",
    "type(x_norm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "直方图："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "counts,  [   7.   21.   42.   97.  120.   91.   64.   38.   17.    3.]\n",
      "bin centers [-2.68067801 -2.13266147 -1.58464494 -1.0366284  -0.48861186  0.05940467\n",
      "  0.60742121  1.15543774  1.70345428  2.25147082  2.79948735]\n"
     ]
    },
    {
     "data": {
      "image/png": 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3As/ut6rJqqqfdIunsXh+8nsrtevt0xaT/HWSbwG7gev6qmMG3gh8qu8itCrfENeIJOcC\nL2BxINWMJE9KcjewANxZVQdXaje1T1tMMg/sWOGmd1XVbVV1DXBNkj3AB4A3TKuWaTjZ8XVtrgEe\nqaobZ1rcBKzl+BrilQEN6KZbPg68rRupN6N7xf8b3fm4TycZVNVwebupBXpVXbrGpjeyCUewJzu+\nJK8HXs3iNfmbzjr+fi14EFh6Yn4ni6N0bRJJngx8AviXqrql73qmpap+kOTfgd9khQ+v6esql/OX\nrF4O7O+jjmlJsgt4B3B5VT3cdz1T1t8HSU/OfwPnJzk3yWnAVcCtPdekNcrih5l/BDhYVR/su55J\nS3Jmkm3d8unApZwgM/u6yuXjwK8CPwW+CfxJVT0080KmJMl9LJ68ePzExeer6uoeS5qoJL8P/ANw\nJvADYH9VvarfqsaT5FXAB/nZG+JOeGnYZpPkJuAS4JeAh4B3V9UN/VY1OUleAnwG+Co/mz7bW1X/\n0V9Vk5PkYmAfiwPwJwEfq6r3r9jWNxZJUhv8TlFJaoSBLkmNMNAlqREGuiQ1wkCXpEYY6JLUCANd\nkhphoEtSI/4P1qxllG6H6EYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa955048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = hist(x_norm)\n",
    "print 'counts, ', h[0]\n",
    "print 'bin centers', h[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "归一化直方图（用出现频率代替次数），将划分区间变为 `20`（默认 `10`）："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xa922eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = hist(x_norm, normed=True, bins=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在这组数据下，正态分布参数的最大似然估计值为："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean,  -0.0426135499965\n",
      "x_std,  0.950754110144\n"
     ]
    }
   ],
   "source": [
    "x_mean, x_std = norm.fit(x_norm)\n",
    "\n",
    "print 'mean, ', x_mean\n",
    "print 'x_std, ', x_std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "将真实的概率密度函数与直方图进行比较："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xDmN4l9acylMYG8IOLas0tLLR6tVw991w663Bhcxrr4V99930cWZj3BDtP12j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\nKZGLiETc/wfoqVYxTpVDEwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1586bf28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = hist(x_norm, normed=True, bins=20)\n",
    "\n",
    "x = linspace(-3,3,50)\n",
    "p = plot(x, norm.pdf(x), 'r-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "导入积分函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.integrate import trapz "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "通过积分，计算落在某个区间的概率大小："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95.45% of the values lie between -2 and 2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x15cbb8d0>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ffML4RYtY4TqIMSVoiCoT9+9nwpAh3PbSS67jhJ2kpCSSkpKKNKbQ0yRFJB5I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\nFXhjjIlSVuCNMSZK/T8+DStxCxquAQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15cbb748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = linspace(-2,2,108)\n",
    "p = trapz(norm.pdf(x1), x1) \n",
    "print '{:.2%} of the values lie between -2 and 2'.format(p)\n",
    "\n",
    "fill_between(x1, norm.pdf(x1), color = 'red')\n",
    "plot(x, norm.pdf(x), 'k-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "默认情况，正态分布的参数为均值0，标准差1，即标准正态分布。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以通过 `loc` 和 `scale` 来调整这些参数，一种方法是调用相关函数时进行输入："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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apZeju9h3Yh/N6jWj5SUtaVW/VdGl5SUtaVm/JU3rNqVxncY0qdOExnUa06hO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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15e78400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = plot(x, norm.pdf(x, loc=0, scale=1))\n",
    "p = plot(x, norm.pdf(x, loc=0.5, scale=2))\n",
    "p = plot(x, norm.pdf(x, loc=-0.5, scale=.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "另一种则是将 `loc, scale` 作为参数直接输给 `norm` 生成相应的分布："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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apZeju9h3Yh/N6jWj5SUtaVW/VdGl5SUtaVm/JU3rNqVxncY0qdOExnUa06hO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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x160ef2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = plot(x, norm(loc=0, scale=1).pdf(x))\n",
    "p = plot(x, norm(loc=0.5, scale=2).pdf(x))\n",
    "p = plot(x, norm(loc=-0.5, scale=.5).pdf(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 其他连续分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.stats import lognorm, t, dweibull"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "支持与 `norm` 类似的操作，如概率密度函数等。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "不同参数的[对数正态分布](https://zh.wikipedia.org/wiki/%E5%AF%B9%E6%95%B0%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83)："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x15781c88>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gq8Bu4FNgmjFmfZs6xcBPjDFTTnKcoAT3116D//gPeOYZuPrqjutsqtjED979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\n9P8BfIyZcbomsyAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x158a85f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(0.01, 3, 100)\n",
    "\n",
    "plot(x, lognorm.pdf(x, 1), label='s=1')\n",
    "plot(x, lognorm.pdf(x, 2), label='s=2')\n",
    "plot(x, lognorm.pdf(x, .1), label='s=0.1')\n",
    "\n",
    "legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "不同的[韦氏分布](https://zh.wikipedia.org/wiki/%E9%9F%A6%E4%BC%AF%E5%88%86%E5%B8%83)："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xaa9bc50>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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dOvDoo4/SvHlzJk6cmG/KvOK23OvWrUuNGjVy9X3nnC8o5V5ISAi1atUqVvq+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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa980d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(0.01, 3, 100)\n",
    "\n",
    "plot(x, dweibull.pdf(x, 1), label='s=1, constant failure rate')\n",
    "plot(x, dweibull.pdf(x, 2), label='s>1, increasing failure rate')\n",
    "plot(x, dweibull.pdf(x, .1), label='0<s<1, decreasing failure rate')\n",
    "\n",
    "legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "不同自由度的[学生 `t` 分布](https://zh.wikipedia.org/wiki/%E5%AD%A6%E7%94%9Ft-%E5%88%86%E5%B8%83)："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x164582e8>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6ytflq11f2SS7e7dI6dIiDx8mQsEUpnVrkblzbZP1D/KXyjMrS2RUpH2D7N4t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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15bb9f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(-3, 3, 100)\n",
    "\n",
    "plot(x, t.pdf(x, 1), label='df=1')\n",
    "plot(x, t.pdf(x, 2), label='df=2')\n",
    "plot(x, t.pdf(x, 100), label='df=100')\n",
    "plot(x[::5], norm.pdf(x[::5]), 'kx', label='normal')\n",
    "\n",
    "legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 离散分布"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "导入离散分布："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.stats import binom, poisson, randint"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "离散分布没有概率密度函数，但是有[概率质量函数](https://zh.wikipedia.org/wiki/%E6%A6%82%E7%8E%87%E8%B4%A8%E9%87%8F%E5%87%BD%E6%95%B0)。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[离散均匀分布](https://zh.wikipedia.org/wiki/%E9%9B%A2%E6%95%A3%E5%9E%8B%E5%9D%87%E5%8B%BB%E5%88%86%E4%BD%88)的概率质量函数（PMF）："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DXpIaYNhLUgMMe0lqgGEvSQ2YGPZJlpKcSPJikntH9DnYtR9LsnMtYyVJl97YsE+yBXgY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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa980fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "high = 10\n",
    "low = -10\n",
    "\n",
    "x = arange(low, high+1, 0.5)\n",
    "p = stem(x, randint(low, high).pmf(x))  # 杆状图"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[二项分布](https://zh.wikipedia.org/wiki/%E4%BA%8C%E9%A0%85%E5%88%86%E4%BD%88)："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1738a198>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WVpafpw2fGlPjs726vjrMkfgvlpN9Skqdz/bU1Mh9ajgaY1aRo6ysjLKysoD3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\naLJXSqk48P8B4O96y1bc/nYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x16550a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_trials = 60\n",
    "x = arange(num_trials)\n",
    "\n",
    "plot(x, binom(num_trials, 0.5).pmf(x), 'o-', label='p=0.5')\n",
    "plot(x, binom(num_trials, 0.2).pmf(x), 'o-', label='p=0.2')\n",
    "\n",
    "legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[泊松分布](https://zh.wikipedia.org/wiki/%E6%B3%8A%E6%9D%BE%E5%88%86%E4%BD%88)："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1763e320>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RSZNEDhxwy2t5xKlTIm++KdKpk6S3aCHjGzYs+rvYbJKemOjrKJU6w547nc+1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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x158c6828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = arange(0,21)\n",
    "\n",
    "plot(x, poisson(1).pmf(x), 'o-', label=r'$\\lambda$=1')\n",
    "plot(x, poisson(4).pmf(x), 'o-', label=r'$\\lambda$=4')\n",
    "plot(x, poisson(9).pmf(x), 'o-', label=r'$\\lambda$=9')\n",
    "\n",
    "legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 自定义离散分布"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "导入要用的函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.stats import rv_discrete"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "一个不均匀的骰子对应的离散值及其概率："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xk = [1, 2, 3, 4, 5, 6]\n",
    "pk = [.3, .35, .25, .05, .025, .025]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义离散分布："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "loaded = rv_discrete(values=(xk, pk))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "此时， `loaded` 可以当作一个离散分布的模块来使用。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "产生两个服从该分布的随机变量："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 1])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loaded.rvs(size=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "产生100个随机变量，将直方图与概率质量函数进行比较："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Container object of 3 artists>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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L2gRcGhFHp+tb5DdjZmYvyJuiISJ2AbumtG2tW/4Fk6diGvY1M7OF4TtZzcwS5YA3M0uU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\niXLAm5klygFvZpYoB7yZWaIc8GZmifp/J4pqDI9mKMcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1764bef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples = loaded.rvs(size=100)\n",
    "bins = linspace(.5,6.5,7)\n",
    "\n",
    "hist(samples, bins=bins, normed=True)\n",
    "stem(xk, loaded.pmf(xk), markerfmt='ro', linefmt='r-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 假设检验"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "导入相关的函数：\n",
    "\n",
    "- 正态分布\n",
    "- 独立双样本 `t` 检验，配对样本 `t` 检验，单样本 `t` 检验\n",
    "- 学生 `t` 分布\n",
    "\n",
    "`t` 检验的相关内容请参考：\n",
    "- 百度百科-`t` 检验：http://baike.baidu.com/view/557340.htm\n",
    "- 维基百科-学生 `t` 检验：https://en.wikipedia.org/wiki/Student%27s_t-test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "from scipy.stats import ttest_ind, ttest_rel, ttest_1samp\n",
    "from scipy.stats import t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 独立样本 t 检验"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "两组参数不同的正态分布："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n1 = norm(loc=0.3, scale=1.0)\n",
    "n2 = norm(loc=0, scale=1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "从分布中产生两组随机样本："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n1_samples = n1.rvs(size=100)\n",
    "n2_samples = n2.rvs(size=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "将两组样本混合在一起："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "samples = hstack((n1_samples, n2_samples)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最大似然参数估计："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "loc, scale = norm.fit(samples)\n",
    "n = norm(loc=loc, scale=scale)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "比较："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x17ca7278>]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GJqySRC5eGTcOMmeGJk1sNtu+HY4ehS+/DL1dA11qQ79dkMPC5BLhPH74ASZN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\nIYRwcpLIhRDCyUkiF0IIJ/d/XdaGnd6OVMIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x17c1c208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(-3,3,100)\n",
    "\n",
    "hist([samples, n1_samples, n2_samples], normed=True)\n",
    "plot(x, n.pdf(x), 'b-')\n",
    "plot(x, n1.pdf(x), 'g-')\n",
    "plot(x, n2.pdf(x), 'r-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "独立双样本 `t` 检验的目的在于判断两组样本之间是否有显著差异："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t = 0.868384594123\n",
      "p-value = 0.386235148899\n"
     ]
    }
   ],
   "source": [
    "t_val, p = ttest_ind(n1_samples, n2_samples)\n",
    "\n",
    "print 't = {}'.format(t_val)\n",
    "print 'p-value = {}'.format(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "`p` 值小，说明这两个样本有显著性差异。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 配对样本 t 检验"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "配对样本指的是两组样本之间的元素一一对应，例如，假设我们有一组病人的数据："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pop_size = 35\n",
    "\n",
    "pre_treat = norm(loc=0, scale=1)\n",
    "n0 = pre_treat.rvs(size=pop_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "经过某种治疗后，对这组病人得到一组新的数据："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "effect = norm(loc=0.05, scale=0.2)\n",
    "eff = effect.rvs(size=pop_size)\n",
    "\n",
    "n1 = n0 + eff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "新数据的最大似然估计："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "loc, scale = norm.fit(n1)\n",
    "post_treat = norm(loc=loc, scale=scale)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "画图："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ngHbuvrK4jmILKynZG2/AL7+UfzBQgHGLxrFi/Qp+27icYzTIdrm5kacDu3eH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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x17ed5fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = figure(figsize=(10,4))\n",
    "\n",
    "ax1 = fig.add_subplot(1,2,1)\n",
    "h = ax1.hist([n0, n1], normed=True)\n",
    "p = ax1.plot(x, pre_treat.pdf(x), 'b-')\n",
    "p = ax1.plot(x, post_treat.pdf(x), 'g-')\n",
    "\n",
    "ax2 = fig.add_subplot(1,2,2)\n",
    "h = ax2.hist(eff, normed=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "独立 `t` 检验："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t = -0.347904839913\n",
      "p-value = 0.728986322039\n"
     ]
    }
   ],
   "source": [
    "t_val, p = ttest_ind(n0, n1)\n",
    "\n",
    "print 't = {}'.format(t_val)\n",
    "print 'p-value = {}'.format(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "高 `p` 值说明两组样本之间没有显著性差异。\n",
    "\n",
    "配对 `t` 检验："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t = -1.89564459709\n",
      "p-value = 0.0665336223673\n"
     ]
    }
   ],
   "source": [
    "t_val, p = ttest_rel(n0, n1)\n",
    "\n",
    "print 't = {}'.format(t_val)\n",
    "print 'p-value = {}'.format(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "配对 `t` 检验的结果说明，配对样本之间存在显著性差异，说明治疗时有效的，符合我们的预期。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `p` 值计算原理 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`p` 值对应的部分是下图中的红色区域，边界范围由 `t` 值决定。 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x179aeac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "my_t = t(pop_size) # 传入参数为自由度，这里自由度为50\n",
    "\n",
    "p = plot(x, my_t.pdf(x), 'b-')\n",
    "lower_x = x[x<= -abs(t_val)]\n",
    "upper_x = x[x>= abs(t_val)]\n",
    "\n",
    "p = fill_between(lower_x, my_t.pdf(lower_x), color='red')\n",
    "p = fill_between(upper_x, my_t.pdf(upper_x), color='red')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}