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Editors-in-chief: Bettina Grün, Torsten Hothorn, Edzer Pebesma, Achim Zeileis    ISSN 1548-7660; CODEN JSSOBK
A Fortran 90 Program for Evaluation of Multivariate Normal and Multivariate t Integrals Over Convex Regions | Somerville | Journal of Statistical Software
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.

Page views:: 7156. Submitted: 1998-01-01. Published: 1999-02-17.
Paper: A Fortran 90 Program for Evaluation of Multivariate Normal and Multivariate t Integrals Over Convex Regions     Download PDF (Downloads: 6888)
Supplements:
mvi3.for: Fortran 90 program Download (Downloads: 2023; 34KB)
wmvi3.exe.zip: wmvi3.exe: Windows Executable Download (Downloads: 1154; 87KB)
qcalc.in.txt: qcalc.in: used for input Download (Downloads: 1923; 1KB)
qcalc.out.txt: qcalc.out: used for output Download (Downloads: 1755; 1KB)
DOI: 10.18637/jss.v003.i04

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