cdf of multivariate normal random numbers

Hi

I want to find the cdf of a set of 1000 bivariate normal random numbers that are generated by

 X=mvnrnd([3,12],[1,.2;.2,1],1000);

To obtain the cdf for a 1d distribution, I can evaluate the cumsum of the probability of each sample after the samples have been sorted in ascending order. But I am confused on how to do this for a bivariate or (for greater dimension) case. I appreciate you help on this.

Answer 1

[Shashank Prasanna]

Did you try mvncdf?

http://www.mathworks.com/help/stats/mvncdf.html

[PChoppala]

To get the cdf I only have X. Is the below piece of code is a correct way of obtaining that (or what you are referring to)?

 X=mvnrnd([3,12],[1,.3;.3,1],625);
 mu=mean(X);
 Sigma=corrcoef(X);

 N=25;
 [X1,X2] = meshgrid(linspace(1,5,N)', linspace(9,15,N)');
 XX = [X1(:) X2(:)];
 C = mvncdf(XX, mu, Sigma);
 contour(X1,X2,reshape(C,N,N));

[Shashank Prasanna]

It is correct for what it is doing. Also, you already have the means and covariance:

[3,12] and [1,0.3;0.3,1]

1) You don't don't have to re estimate them you can use them directly.

2) MVNCDF expects the Covariance and not correlation matrix. Use COV function instead.