C++与正态分布

  1 // NormalDistribution.cpp : Defines the entry point for the console application. 
  2 // 
  3 #include <stdio.h> 
  4 #include <tchar.h> 
  5 #include <iostream> 
  6 #include <windows.h> 
  7 #include <algorithm> 
  8 #define _USE_MATH_DEFINES 
  9 #include <math.h> 
 10 using namespace std; 
 11 
 12 
 13 // 高斯分布随机数系列,默认期望值为0,方差为1
 14 double GaussRand(double dExpect = 0, double dVariance = 1);
 15 double GaussRand(double dExpect, double dVariance)
 16 {
 17     static double V1, V2, S;
 18     static int phase = 0;
 19     double X;
 20 
 21     if ( phase == 0 )
 22     {
 23         do
 24         {
 25             double U1 = (double)rand() / RAND_MAX;
 26             double U2 = (double)rand() / RAND_MAX;
 27 
 28             V1 = 2 * U1 - 1;
 29             V2 = 2 * U2 - 1;
 30             S = V1 * V1 + V2 * V2;
 31         } while(S >= 1 || S == 0);
 32 
 33         X = V1 * sqrt(-2 * log(S) / S);
 34     }
 35     else
 36     {
 37         X = V2 * sqrt(-2 * log(S) / S);
 38     }
 39 
 40     phase = 1 - phase;
 41 
 42     return (X*dVariance + dExpect);
 43 }
 44 
 45 int _tmain(int argc, _TCHAR* argv[]) 
 46 { 
 47     const int DATA_CNT = 100000; 
 48     double dArrData[DATA_CNT] = {0}; 
 49 
 50     double dSum = 0; 
 51 
 52     // 对所有数赋随机数,默认期望值为0,方差为1
 53     srand(GetTickCount()); 
 54     for (int nIdx = 0; nIdx < DATA_CNT; nIdx++) 
 55     { 
 56         // 防止计算方差时数值过大 
 57         dArrData[nIdx] = GaussRand(); 
 58         dSum += dArrData[nIdx]; 
 59     } 
 60 
 61     // 求平均数 
 62     double dAverageData = dSum / DATA_CNT; 
 63 
 64     // 计算所有的数的方差(各个数据分别与其和的平均数之差的平方的和的平均数) 
 65     double dVariance = 0.0; 
 66     for (int nIdx = 0; nIdx < DATA_CNT; nIdx++) 
 67     { 
 68         double dDeviate = dArrData[nIdx] - dAverageData; 
 69         dVariance += pow(dDeviate, 2); 
 70     } 
 71     dVariance /= DATA_CNT; 
 72 
 73     // 计算标准差(方差的算术平方根,反映一组数据的离散程序) 
 74     double dStandardDeviation = sqrt(dVariance); 
 75 
 76     // 计算0.5个正负标准差之间包含的数字个数 
 77     int nDataCnt = 0; 
 78     for (int nIdx = 0; nIdx < DATA_CNT; nIdx++) 
 79     { 
 80         double dDeviate = dArrData[nIdx] - dAverageData; 
 81         if (abs(dDeviate) <= 0.5*dStandardDeviation) 
 82         { 
 83             nDataCnt++; 
 84         } 
 85     } 
 86     cout<<nDataCnt<<endl; 
 87 
 88     // 计算1个正负标准差之间包含的数字个数 
 89     nDataCnt = 0;
 90     for (int nIdx = 0; nIdx < DATA_CNT; nIdx++) 
 91     { 
 92         double dDeviate = dArrData[nIdx] - dAverageData; 
 93         if (abs(dDeviate) <= dStandardDeviation) 
 94         { 
 95             nDataCnt++; 
 96         } 
 97     } 
 98     cout<<nDataCnt<<endl; 
 99 
100     // 计算2个正负标准差之间包含的数字个数 
101     nDataCnt = 0;
102     for (int nIdx = 0; nIdx < DATA_CNT; nIdx++) 
103     { 
104         double dDeviate = dArrData[nIdx] - dAverageData; 
105         if (abs(dDeviate) <= 2*dStandardDeviation) 
106         { 
107             nDataCnt++; 
108         } 
109     } 
110     cout<<nDataCnt<<endl; 
111 
112     // 计算3个正负标准差之间包含的数字个数 
113     nDataCnt = 0;
114     for (int nIdx = 0; nIdx < DATA_CNT; nIdx++) 
115     { 
116         double dDeviate = dArrData[nIdx] - dAverageData; 
117         if (abs(dDeviate) <= 3*dStandardDeviation) 
118         { 
119             nDataCnt++; 
120         } 
121     } 
122     cout<<nDataCnt<<endl; 
123 
124     return 0; 
125 }