Cumulative density of multivariate normal distribution

[ErinYume]

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!

[Ksharp]

Calling @Rick_SAS 

[Rick_SAS]

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.

[mgx]

Dear Rick,

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

[Rick_SAS]

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."