topic Multivariate Normal Tail probabilities in SAS/IML Software and Matrix Computations

Multivariate Normal Tail probabilities

TomTom — Tue, 10 Jan 2012 16:20:02 GMT

Hello,

I was wondering whether there is a SAS/IML function for obtaining tail probabilities of a multivariate Normal RV? Rick has blogged extensively about sampling from a MVN (thanks Rick!) but I can’t find anything about tail probabilities.In essence I am looking for what this package provides in R:

http://cran.r-project.org/web/packages/mnormt/mnormt.pdf

Many thanks

Multivariate Normal Tail probabilities

Rick_SAS — Tue, 10 Jan 2012 20:01:17 GMT

For 1D, use the CDF function. For 2D, use the PROBBNRM function. For higher dimensions, Genz's 1992 algorithm was implemented in IML by Bretz: http://www.biostat.uni-hannover.de/89.html Somerville and Bretz also have a 2001 algorithm that is available on the same web site.

I haven't used the high-D algorithms, so I can't speak to their efficiency.

Rick

Re: Multivariate Normal Tail probabilities

TomTom — Tue, 10 Jan 2012 21:01:52 GMT

Thanks for your reply. I was aware of the Genz & Bretz modules but hoped that there was a (hidden) build-in function that I missed.