# cdf of multivariate normal random numbers

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PChoppala on 8 Aug 2013
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.

Shashank Prasanna on 8 Aug 2013

PChoppala on 8 Aug 2013
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 on 8 Aug 2013
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.