# C++与正态分布

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div id=”content” contentScore=”4664″>

// NormalDistribution.cpp : Defines the entry point for the console application.
//
#include <stdio.h>
#include <tchar.h>
#include
#include <windows.h>
#include
#define _USE_MATH_DEFINES
#include <math.h>
using namespace std;

// 高斯分布随机数系列,默认期望值为0,方差为1
double GaussRand(double dExpect = 0, double dVariance = 1);
double GaussRand(double dExpect, double dVariance)
{
static double V1, V2, S;
static int phase = 0;
double X;

if ( phase == 0 )
{
do
{
double U1 = (double)rand() / RAND_MAX;
double U2 = (double)rand() / RAND_MAX;

V1 = 2 * U1 – 1;
V2 = 2 * U2 – 1;
S = V1 * V1 + V2 * V2;
} while(S >= 1 || S == 0);

X = V1 * sqrt(-2 * log(S) / S);
}
else
{
X = V2 * sqrt(-2 * log(S) / S);
}

phase = 1 – phase;

return (X*dVariance + dExpect);
}

int _tmain(int argc, _TCHAR* argv[])
{
const int DATA_CNT = 100000;
double dArrData[DATA_CNT] = {0};

double dSum = 0;

// 对所有数赋随机数,默认期望值为0,方差为1
srand(GetTickCount());
for (int nIdx = 0; nIdx < DATA_CNT; nIdx++)
{
// 防止计算方差时数值过大
dArrData[nIdx] = GaussRand();
dSum += dArrData[nIdx];
}

// 求平均数
double dAverageData = dSum / DATA_CNT;

// 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)
double dVariance = 0.0;
for (int nIdx = 0; nIdx < DATA_CNT; nIdx++)
{
double dDeviate = dArrData[nIdx] – dAverageData;
dVariance += pow(dDeviate, 2);
}
dVariance /= DATA_CNT;

// 计算标准差(方差的算术平方根,反映一组数据的离散程序)
double dStandardDeviation = sqrt(dVariance);

// 计算0.5个正负标准差之间包含的数字个数
int nDataCnt = 0;
for (int nIdx = 0; nIdx < DATA_CNT; nIdx++)
{
double dDeviate = dArrData[nIdx] – dAverageData;
if (abs(dDeviate) <= 0.5*dStandardDeviation)
{
nDataCnt++;
}
}
cout<<nDataCnt<<endl;

// 计算1个正负标准差之间包含的数字个数
nDataCnt = 0;
for (int nIdx = 0; nIdx < DATA_CNT; nIdx++)
{
double dDeviate = dArrData[nIdx] – dAverageData;
if (abs(dDeviate) <= dStandardDeviation)
{
nDataCnt++;
}
}
cout<<nDataCnt<<endl;

// 计算2个正负标准差之间包含的数字个数
nDataCnt = 0;
for (int nIdx = 0; nIdx < DATA_CNT; nIdx++)
{
double dDeviate = dArrData[nIdx] – dAverageData;
if (abs(dDeviate) <= 2*dStandardDeviation)
{
nDataCnt++;
}
}
cout<<nDataCnt<<endl;

// 计算3个正负标准差之间包含的数字个数
nDataCnt = 0;
for (int nIdx = 0; nIdx < DATA_CNT; nIdx++)
{
double dDeviate = dArrData[nIdx] – dAverageData;
if (abs(dDeviate) <= 3*dStandardDeviation)
{
nDataCnt++;
}
}
cout<<nDataCnt<<endl;

return 0;
}

(附)标准正态分布表

φ( – x ) = 1 φx )

 x 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0 0.500 0 0.504 0 0.508 0 0.512 0 0.516 0 0.519 9 0.523 9 0.527 9 0.531 9 0.535 9 0.1 0.539 8 0.543 8 0.547 8 0.551 7 0.555 7 0.559 6 0.563 6 0.567 5 0.571 4 0.575 3 0.2 0.579 3 0.583 2 0.587 1 0.591 0 0.594 8 0.598 7 0.602 6 0.606 4 0.610 3 0.614 1 0.3 0.617 9 0.621 7 0.625 5 0.629 3 0.633 1 0.636 8 0.640 4 0.644 3 0.648 0 0.651 7 0.4 0.655 4 0.659 1 0.662 8 0.666 4 0.670 0 0.673 6 0.677 2 0.680 8 0.684 4 0.687 9 0.5 0.691 5 0.695 0 0.698 5 0.701 9 0.705 4 0.708 8 0.712 3 0.715 7 0.719 0 0.722 4 0.6 0.725 7 0.729 1 0.732 4 0.735 7 0.738 9 0.742 2 0.745 4 0.748 6 0.751 7 0.754 9 0.7 0.758 0 0.761 1 0.764 2 0.767 3 0.770 3 0.773 4 0.776 4 0.779 4 0.782 3 0.785 2 0.8 0.788 1 0.791 0 0.793 9 0.796 7 0.799 5 0.802 3 0.805 1 0.807 8 0.810 6 0.813 3 0.9 0.815 9 0.818 6 0.821 2 0.823 8 0.826 4 0.828 9 0.835 5 0.834 0 0.836 5 0.838 9 1 0.841 3 0.843 8 0.846 1 0.848 5 0.850 8 0.853 1 0.855 4 0.857 7 0.859 9 0.862 1 1.1 0.864 3 0.866 5 0.868 6 0.870 8 0.872 9 0.874 9 0.877 0 0.879 0 0.881 0 0.883 0 1.2 0.884 9 0.886 9 0.888 8 0.890 7 0.892 5 0.894 4 0.896 2 0.898 0 0.899 7 0.901 5 1.3 0.903 2 0.904 9 0.906 6 0.908 2 0.909 9 0.911 5 0.913 1 0.914 7 0.916 2 0.917 7 1.4 0.919 2 0.920 7 0.922 2 0.923 6 0.925 1 0.926 5 0.927 9 0.929 2 0.930 6 0.931 9 1.5 0.933 2 0.934 5 0.935 7 0.937 0 0.938 2 0.939 4 0.940 6 0.941 8 0.943 0 0.944 1 1.6 0.945 2 0.946 3 0.947 4 0.948 4 0.949 5 0.950 5 0.951 5 0.952 5 0.953 5 0.953 5 1.7 0.955 4 0.956 4 0.957 3 0.958 2 0.959 1 0.959 9 0.960 8 0.961 6 0.962 5 0.963 3 1.8 0.964 1 0.964 8 0.965 6 0.966 4 0.967 2 0.967 8 0.968 6 0.969 3 0.970 0 0.970 6 1.9 0.971 3 0.971 9 0.972 6 0.973 2 0.973 8 0.974 4 0.975 0 0.975 6 0.976 2 0.976 7 2 0.977 2 0.977 8 0.978 3 0.978 8 0.979 3 0.979 8 0.980 3 0.980 8 0.981 2 0.981 7 2.1 0.982 1 0.982 6 0.983 0 0.983 4 0.983 8 0.984 2 0.984 6 0.985 0 0.985 4 0.985 7 2.2 0.986 1 0.986 4 0.986 8 0.987 1 0.987 4 0.987 8 0.988 1 0.988 4 0.988 7 0.989 0 2.3 0.989 3 0.989 6 0.989 8 0.990 1 0.990 4 0.990 6 0.990 9 0.991 1 0.991 3 0.991 6 2.4 0.991 8 0.992 0 0.992 2 0.992 5 0.992 7 0.992 9 0.993 1 0.993 2 0.993 4 0.993 6 2.5 0.993 8 0.994 0 0.994 1 0.994 3 0.994 5 0.994 6 0.994 8 0.994 9 0.995 1 0.995 2 2.6 0.995 3 0.995 5 0.995 6 0.995 7 0.995 9 0.996 0 0.996 1 0.996 2 0.996 3 0.996 4 2.7 0.996 5 0.996 6 0.996 7 0.996 8 0.996 9 0.997 0 0.997 1 0.997 2 0.997 3 0.997 4 2.8 0.997 4 0.997 5 0.997 6 0.997 7 0.997 7 0.997 8 0.997 9 0.997 9 0.998 0 0.998 1 2.9 0.998 1 0.998 2 0.998 2 0.998 3 0.998 4 0.998 4 0.998 5 0.998 5 0.998 6 0.998 6 x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 3 0.998 7 0.999 0 0.999 3 0.999 5 0.999 7 0.999 8 0.999 8 0.999 9 0.999 9 1.000 0

(附)正态分布概率表

C++ Primer Plus 第6版 中文版 清晰有书签PDF+源代码 http://www.linuxidc.com/Linux/2014-05/101227.htm

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• Linux-C成长之路（七）：数组与指针 http://www.linuxidc.com/Linux/2014-05/101242p7.htm
• Linux-C成长之路（八）：存储类，动态内存 http://www.linuxidc.com/Linux/2014-05/101242p8.htm
• Linux-C成长之路（九）：复合数据类型 http://www.linuxidc.com/Linux/2014-05/101242p9.htm
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