How to use mvnrnd function ?

How to use mvnrnd function ?

I need to generate a matrix whose elements follow normal distribution with zero mean and Q covariance matrix . I know Q (some positive definite matrix)

I'm using the following code

Q size is (4,4) MU=zeros(1,4); noise=mvnrnd(MU,Q,10)+1j*mvnrnd(MU,Q,10);

MY noise size should be (4,10) but i m getting size as (10,4)

Thanks

Answer 1

[Alka Nair]

The documentation of MVNRND suggests that the syntax is

>> r = mvnrnd(MU,SIGMA,cases) and r = mvnrnd(MU,SIGMA,cases) returns a cases-by-d matrix R of random vectors chosen from the multivariate normal distribution with a common 1-by-d mean vector MU, and a common d-by-d covariance matrix SIGMA. As cases is 10 in your case and d is 4, you are observing the dimension 10*4 for 'noise'.

Please refer to the documentation at:

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

[Betha Shirisha]

@ Alka Nair thanks..:)

But if r is of size (cases,d),then it's covariance matrix will be of size (cases,cases)..then sigma should also be of size (cases,cases),right ?

[John D'Errico]

No, no no.

cases, the third argument is the NUMBER of samples to be generated. Those samples are independent of each other.

The covariance matrix is the covariance of those random variables, but not from sample to sample. Again, the samples are INDEPENDENT.

So if the random variable lives in a d-dimensional space, then you will need to pass in a vector of length d for mu, and a matrix of size dxd for sigma. Then expect that the result will be of size (cases,d).

[Betha Shirisha]

@ john thanks..