I am trying to create a bivariate normal distribution of random numbers in Matlab that is symmetrical. I know the standard deviation of the gaussian (15 for example) and that it is the same in both directions. How do I use this standard deviation information to get the covariance in a form that Matlab will accept for the mvnrnd command? Thanks, I would really appreciate any advice.
我试图在Matlab中创建一个对称的随机数的双变量正态分布。我知道高斯的标准偏差（例如15），并且它在两个方向上都是相同的。如何使用此标准差信息以Matlab将接受mvnrnd命令的形式获得协方差？谢谢，我真的很感激任何建议。
3 个解决方案
#1
1
First of all, you need to know the correlation between the two normal variables. Like @Luis said, the diagonal will be 15 each but for the covariance, you need to know the correlation between both.
首先，您需要知道两个正常变量之间的相关性。就像@Luis所说的那样，对角线将是15，但对于协方差，你需要知道两者之间的相关性。
They are related by this equation:
它们与以下等式相关：
cov(x,y) = correlation(x,y)*std(x)*std(y)
But if you do not know the correlation, then you can calculate the sample covariance.
但如果您不知道相关性，则可以计算样本协方差。
Forumla for sample covariance:
Forumla样本协方差：
To calculate in Matlab:
要在Matlab中计算：
cov = (1/n)*(x-mean(x))*(y-mean(y))'
With reference to:http://www.cogsci.ucsd.edu/~desa/109/trieschmarksslides.pdf
参考：http：//www.cogsci.ucsd.edu/~desa/109/trieschmarksslides.pdf
#2
1
If the random variables are independent, the off-diaginal elements of the covariance matrix are zero. So that matrix will be diag(std1,std2), where std1 and std2 are the standard deviations of your two variables. In your example you would use diag(15,15).
如果随机变量是独立的，则协方差矩阵的偏外元素为零。因此矩阵将是diag（std1，std2），其中std1和std2是两个变量的标准偏差。在你的例子中，你将使用diag（15,15）。
If the random variables are not independent, you need to specify all four elements of the covariance matrix.
如果随机变量不是独立的，则需要指定协方差矩阵的所有四个元素。
#3
0
You can use the command cov in Matlab:
您可以在Matlab中使用命令cov：
SIGMA = cov([x y]);
HTH
HTH
#1
1
First of all, you need to know the correlation between the two normal variables. Like @Luis said, the diagonal will be 15 each but for the covariance, you need to know the correlation between both.
首先，您需要知道两个正常变量之间的相关性。就像@Luis所说的那样，对角线将是15，但对于协方差，你需要知道两者之间的相关性。
They are related by this equation:
它们与以下等式相关：
cov(x,y) = correlation(x,y)*std(x)*std(y)
But if you do not know the correlation, then you can calculate the sample covariance.
但如果您不知道相关性，则可以计算样本协方差。
Forumla for sample covariance:
Forumla样本协方差：
To calculate in Matlab:
要在Matlab中计算：
cov = (1/n)*(x-mean(x))*(y-mean(y))'
With reference to:http://www.cogsci.ucsd.edu/~desa/109/trieschmarksslides.pdf
参考：http：//www.cogsci.ucsd.edu/~desa/109/trieschmarksslides.pdf
#2
1
If the random variables are independent, the off-diaginal elements of the covariance matrix are zero. So that matrix will be diag(std1,std2), where std1 and std2 are the standard deviations of your two variables. In your example you would use diag(15,15).
如果随机变量是独立的，则协方差矩阵的偏外元素为零。因此矩阵将是diag（std1，std2），其中std1和std2是两个变量的标准偏差。在你的例子中，你将使用diag（15,15）。
If the random variables are not independent, you need to specify all four elements of the covariance matrix.
如果随机变量不是独立的，则需要指定协方差矩阵的所有四个元素。
#3
0
You can use the command cov in Matlab:
您可以在Matlab中使用命令cov：
SIGMA = cov([x y]);
HTH
HTH