根据均匀分布生成正态分布

 

Box-Muller算法
先贴出来代码，后面给出详细证明过程

#include<stdafx.h>
#include<math.h>
#include<assert.h>

#include<stdlib.h>

#include<iostream>
#include<time.h>
using namespace std;

class ALL_DISTRIBUTE
{
public:
	static double standartDis(int ave, double delta);

	static double __rand(void);

};

//产生一个[0-1]的均匀随机数
double ALL_DISTRIBUTE::__rand(void)
{
	int ret = rand() % 32767;
	double res = (32767.0 - ret) / 32767;
	return res;
}

double ALL_DISTRIBUTE::standartDis(int ave, double delta)
{
	double random_1 = __rand();
	double random_2 = __rand();
	double res = 0;
	if (delta <=0 )
	{
		assert(0);
	}
	res = sqrt(delta)*sqrt(-2 * log(random_1))*cos(2*3.14*random_2) + ave;
	return res;
}
int main(int argc, char** argv)
{
	srand(time(NULL) * 100);

	for (int i = 0; i<100; i++)
	{
		cout << ALL_DISTRIBUTE::standartDis(1, 0.01) << endl;
	}
}