Methods for the Computation of Multivariate t-Probabilities (2000)
| Venue: | Computing Sciences and Statistics |
| Citations: | 31 - 8 self |
BibTeX
@ARTICLE{Genz00methodsfor,
author = {Alan Genz and Frank Bretz},
title = {Methods for the Computation of Multivariate t-Probabilities},
journal = {Computing Sciences and Statistics},
year = {2000},
volume = {25},
pages = {400--405}
}
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Abstract
This paper compares methods for the numerical computation of multivariate t-probabilities for hyperrectangular integration regions. Methods based on acceptance-rejection, spherical-radial transformations and separation-of-variables transformations are considered. Tests using randomly chosen problems show that the most efficient numerical methods use a transformation developed by Genz (1992) for multivariate normal probabilities. These methods allow moderately accurate multivariate t-probabilities to be quickly computed for problems with as many as twenty variables. Methods for the non-central multivariate t-distribution are also described. Key Words: multivariate t-distribution, non-central distribution, numerical integration, statistical computation. 1 Introduction A common problem in many statistics applications is the numerical computation of the multivariate t (MVT) distribution function (see Tong, 1990) defined by T(a; b; \Sigma; ) = \Gamma( +m 2 ) \Gamma( 2 ) p j\Sigma...
