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A Fortran 90 Program for Evaluation of Multivariate Normal and Multivariate t Integrals Over Convex Regions

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  • Somerville, Paul N.

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.

Suggested Citation

  • Somerville, Paul N., 1999. "A Fortran 90 Program for Evaluation of Multivariate Normal and Multivariate t Integrals Over Convex Regions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 3(i04).
    • Handle: RePEc:jss:jstsof:v:003:i04
    DOI: http://hdl.handle.net/10.18637/jss.v003.i04
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    References listed on IDEAS

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    1. Olson, Jane M. & Weissfeld, Lisa A., 1991. "Approximation of certain multivariate integrals," Statistics & Probability Letters, Elsevier, vol. 11(4), pages 309-317, April.
    2. Somerville, Paul N., 1997. "Multiple testing and simultaneous confidence intervals: calculation of constants," Computational Statistics & Data Analysis, Elsevier, vol. 25(2), pages 217-233, July.
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