将正态随机变量与任意 RHO(corrcoef） 相关联

correlated normal random variables with arbitrary rho(corrcoef)

本文关键字：corrcoef 关联 RHO 任意 随机 变量      更新时间：2023-10-16

>我对生成相关随机变量有疑问...有没有办法生成 x1(0， 1(， x2(0， 1(，这些 rho = 0 是正常的;或生成 x3(0， 1(， x4(0， 1( 让 rho = 0.75 还是别的什么？

到目前为止我试过了

1-独立正常发电机：

vector<double> uncorr_normal(double m, double s, int n)
{
random_device seed;
mt19937 gen{ seed() };
normal_distribution<> dist{ m, s };
vector<double> samples;
for (int i = 0; i < n; i++)
{
samples.push_back(dist(gen));
}
return samples;
}

2- 依赖型普通发电机：

pair<vector<double>, vector<double>> 
corr_normal(double m1, double s1, double m2, double s2, double rho, int n)
{
vector<double> X;
vector<double> Y;
random_device seed;
mt19937 gen{ seed() };
normal_distribution<> dist1{ m1, s1 };
normal_distribution<> dist2{ m2, s2 };
for (int i = 0; i < n; i++)
{
double x = dist1(gen);
X.push_back(x);
double y = rho * x + sqrt(1 - rho * rho) * dist2(gen);
Y.push_back(y);
}
pair<vector<double>, vector<double>> pair(X, Y);
return pair;

}

我通过下面实现的函数来测量相关系数：

double rho(vector<double>& X, vector<double>& Y)
{
double sum_X = 0, sum_Y = 0, sum_XY = 0;
double squareSum_X = 0, squareSum_Y = 0;
//------------------------------------------
size_t n = max(X.size(), Y.size());
//------------------------------------------
for (int i = 0; i < n; i++)
{
// sum of elements of array X.
sum_X = sum_X + X[i];
// sum of elements of array Y.
sum_Y = sum_Y + Y[i];
// sum of X[i] * Y[i].
sum_XY = sum_XY + X[i] * Y[i];
// sum of square of array elements.
squareSum_X = squareSum_X + X[i] * X[i];
squareSum_Y = squareSum_Y + Y[i] * Y[i];
}
// use formula for calculating correlation coefficient.
double corr = (double)(n * sum_XY - sum_X * sum_Y)
/ (double)(sqrt((n * squareSum_X - sum_X * sum_X)
* (n * squareSum_Y - sum_Y * sum_Y)));
//------------------------------------------
return corr;

}

但是，如果我生成两个不相关的随机变量并使用 rho 函数测试它们，则不会得到 rho = 0;

对于相关情况，如果我插入随机相关向量，我也不会得到指定的 RHO。

你能帮我这个吗？

此致敬意

在相关情况下，您必须创建标准正态样本，然后转换并关联它们：

pair<vector<double>, vector<double>>
corr_normal(double m1, double s1, double m2, double s2, double rho, int n)
{
vector<double> X;
vector<double> Y;
random_device seed;
mt19937 gen{ seed() };
normal_distribution<> dist1{ 0.0, 1.0 };
normal_distribution<> dist2{ 0.0, 1.0 };
for (int i = 0; i < n; i++)
{
double x = dist1(gen);
X.push_back(m1 + x * s1);
double y = m2 + s2*(rho * x + sqrt(1 - rho * rho) * dist2(gen));
Y.push_back(y);
}
pair<vector<double>, vector<double>> pair(X, Y);
return pair;
}

请参阅 http://www.statisticalengineering.com/bivariate_normal.htm

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