*! version 1.0 16 Apr 2015

Title

mvnormal -- Multivariate Normal Distribution

Syntax

mvnormal
[,
options]

Main
lower(numlist miss) The vector of lower limits of length k. Use . to indicate a value is -Infinity.

upper(numlist miss) The vector of upper limits of length k. Use . to indicate a value is +Infinity.

mean(numlist) The mean vector of length k. No missing values allowed.

sigma(string) The covariance matrix of dimension k. Must be symmetric positive-definite.

shifts(#) The number of shifts of the Quasi-Monte Carlo integration algorithm to use. Must be a strictly positive integer. Defaults to 12.

samples(#) The number of samples in each shift of the Quasi-Monte Carlo integration algorithm to use. Must be a strictly positive integer. Defaults to 1000.

alpha(#) The value of the Monte Carlo confidence factor to use. Must be strictly positive. Defaults to 3.

Description

mvnormal computes the distribution function of the multivariate normal distribution for arbitrary limits, mean vectors and correlation matrices.

Options

Main

lower(numlist miss) The vector of lower limits of length k. Use . to indicate a value is -Infinity.

upper(numlist miss) The vector of upper limits of length k. Use . to indicate a value is +Infinity.

mean(numlist) The mean vector of length k. No missing values allowed.

sigma(string) The covariance matrix of dimension k. Must be symmetric positive-definite.

shifts(#) The number of shifts of the Quasi-Monte Carlo integration algorithm to use. Must be a strictly positive integer. Defaults to 12.

samples(#) The number of samples in each shift of the Quasi-Monte Carlo integration algorithm to use. Must be a strictly positive integer. Defaults to 1000.

alpha(#) The value of the Monte Carlo confidence factor to use. Must be strictly positive. Defaults to 3.

Examples

mat Sigma = (1, 0.5, 0.5 \ 0.5, 1, 0.5 \ 0.5, 0.5, 1)

mvnormal, lower(-2.06, -2.06, -2.06) upper(2.06, 2.06, 2.06) mean(0, 0, 0) sigma(Sigma)

Authors

Michael J. Grayling & Adrian P. Mander,
MRC Biostatistics Unit, Cambridge, UK.

Email mjg211@cam.ac.uk

See Also

References:

Genz A (1992) Numerical Computation of Multivariate Normal Probabilities.
Journal of Computational and Graphical Statistics. 1: 141–150.
Genz A, Bretz F (2009) Computation of Multivariate Normal and t Probabilities.
Lecture Notes in Statistics, Vol 195. Springer-Verlag: Heidelberg, Germany.
Tong YL (2012) The Multivariate Normal Distribution. Springer-Verlag: New York,
US.

Related commands:

mvnormalden (if installed)
rmvnormal (if installed)
invmvnormal (if installed)