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| Authors: | Paul N. Somerville | ||||||||
| Title: | A Fortran 90 Program for Evaluation of Multivariate Normal and Multivariate t Integrals Over Convex Regions | ||||||||
| Abstract: | Let X' = (X1,X2, ... ,Xk) have the multivariate normal distribution f(X) = MVN(μ, ∑σ2) where ∑ is a known positive definite matrix, and σ2 is a constant. There are many problems in statistics which require the evaluation of f(x) over some convex region A. That is P = ∫A f(X) dX. If σ2 is known, then without loss of generality, set μ = 0, σ =1 and let ∑ be the correlation matrix. For the case where the region A is rectangular, the problem has been addressed by many authors. They include Gupta (1963), Milton (1972), Schervish (1984), Deak (1986), Wang and Kennedy (1990,1992), Olson and Weissfeld (1991), Drezner (1992) and Genz (1992,1993). However, regions of integration for many statistical applications, for example multiple comparisons, are not rectangular. |
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Page views:: 7834. Submitted: 1998-01-01. Published: 1999-02-17. |
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| Paper: |
A Fortran 90 Program for Evaluation of Multivariate Normal and Multivariate t Integrals Over Convex Regions
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| DOI: |
10.18637/jss.v003.i04
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This work is licensed under the licenses Paper: Creative Commons Attribution 3.0 Unported License Code: GNU General Public License (at least one of version 2 or version 3) or a GPL-compatible license. |