ch02prob.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np            # 数値計算\n",
    "import scipy  as sp              # 数学・科学技術計算"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 確率の考え方"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 3, 3, 2, 4, 5, 3, 6, 6, 6])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.choice(np.arange(1,7),10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6, 5, 3, 2, 4])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.choice(np.arange(1,7),5,replace=False)  # 非復元抽出"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 1, 6, 3, 1])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.choice(np.arange(1,7),5)                # 復元抽出"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6, 6, 5, 1, 5, 6, 6, 4, 6, 1])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = np.array([1,1,1,3,3,3]); p = p/np.sum(p)\n",
    "np.random.choice(np.arange(1,7),10, p=p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 期待値と分散"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2437536083479015"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.random.normal(1,2,100)     # 期待値1，標準偏差2の正規分布にしたがうデータを100個生成   \n",
    "x.mean()                          # データの平均値を計算．np.mean(x) と同じ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.7079682530577351"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.std()                           # データの標準偏差を計算．np.std(x) と同じ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.64000000000000001"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.abs(x-np.mean(x)) <= np.std(x))    # |x-E[x]]| ≦ sd(x) となるデータの割合"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.94999999999999996"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.abs(x-np.mean(x)) <= 2*np.std(x))  # |x-E[x]]| ≦ 2*sd(x) となるデータの割合"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 分位点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.52440051270804067"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import norm    # sp.stats.normを使う\n",
    "sp.stats.norm.ppf(0.7)               # N(0,1)の 0.7点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0488010254160813"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.stats.norm.ppf(0.7,loc=1,scale=2) # N(1,2**2)の 0.7点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6448536269514722"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha = 0.05\n",
    "sp.stats.norm.ppf(1-alpha) # N(0,1)の上側0.05点"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 共分散・相関係数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(150, 4)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "iris = load_iris()\n",
    "iris.data.shape            # データ数150, 次元4 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.68569351, -0.03926846,  1.27368233,  0.5169038 ],\n",
       "       [-0.03926846,  0.18800403, -0.32171275, -0.11798121],\n",
       "       [ 1.27368233, -0.32171275,  3.11317942,  1.29638747],\n",
       "       [ 0.5169038 , -0.11798121,  1.29638747,  0.58241432]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cov(iris.data.T)        # 分散共分散行列(データ行列の転置を入れる)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        , -0.10936925,  0.87175416,  0.81795363],\n",
       "       [-0.10936925,  1.        , -0.4205161 , -0.35654409],\n",
       "       [ 0.87175416, -0.4205161 ,  1.        ,  0.9627571 ],\n",
       "       [ 0.81795363, -0.35654409,  0.9627571 ,  1.        ]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(iris.data.T)   # 相関係数行列(データ行列の転置を入れる)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}