topic Re: Cumulative density of multivariate normal distribution in SAS Programming

Cumulative density of multivariate normal distribution

ErinYume — Wed, 08 Apr 2020 01:41:45 GMT

Hi all,

I am trying to compute a probability of a multivariate distribution up to a vector of values. For example, I want to obtain the probability of a 4-variable multivariate distribution up to point (x1,x2,x3,x4). How can I achieve this goal? I am using sas enterprise guide.

Thanks!

Re: Cumulative density of multivariate normal distribution

Ksharp — Wed, 08 Apr 2020 10:47:18 GMT

Calling @Rick_SAS

Re: Cumulative density of multivariate normal distribution

Rick_SAS — Wed, 08 Apr 2020 11:02:42 GMT

For the bivariate normal CDF, you can use the PROBBNRM function to compute the cumulative probabilities.

In higher dimensions, there is no built-in support for the high-dimensional semi-infinite integrals that are needed for a general multivariate normal (MVN) with correlated variables.

What is the covariance matrix for your MVN? For some structured matrices, we might be able to suggest a solution.

Re: Cumulative density of multivariate normal distribution

mgx — Wed, 06 Mar 2024 10:07:34 GMT

Dear Rick,

I have the same question. Is there a built-in function developed for multivariate normal distributions in the meantime?

Re: Cumulative density of multivariate normal distribution

Rick_SAS — Wed, 06 Mar 2024 10:49:03 GMT

You can evaluate the multivariate normal density (PDF) and generate random variates for any dimension. But SAS provides a d-dimensional normal CDF only for d=1 (CDF("Normal") and d=2 (PROBBNRM). For more about the 2-D case, see the article, "Bivariate normal probability in SAS."