{smcl} {* *! version 1.0 16 Apr 2015}{...} {vieweralsosee "" "--"}{...} {vieweralsosee "Install command2" "ssc install command2"}{...} {vieweralsosee "Help command2 (if installed)" "help command2"}{...} {viewerjumpto "Syntax" "mvnormal##syntax"}{...} {viewerjumpto "Description" "mvnormal##description"}{...} {viewerjumpto "Options" "mvnormal##options"}{...} {viewerjumpto "Remarks" "mvnormal##remarks"}{...} {viewerjumpto "Examples" "mvnormal##examples"}{...} {title:Title} {phang} {bf:mvnormal} {hline 2} Multivariate Normal Distribution {marker syntax}{...} {title:Syntax} {p 8 17 2} {cmdab:mvnormal} [{cmd:,} {it:options}] {synoptset 20 tabbed}{...} {synopthdr} {synoptline} {syntab:Main} {synopt:{opt low:er(numlist miss)}} The vector of lower limits of length k. Use . to indicate a value is -Infinity.{p_end} {synopt:{opt upp:er(numlist miss)}} The vector of upper limits of length k. Use . to indicate a value is +Infinity.{p_end} {synopt:{opt me:an(numlist)}} The mean vector of length k. No missing values allowed.{p_end} {synopt:{opt s:igma(string)}} The covariance matrix of dimension k. Must be symmetric positive-definite.{p_end} {synopt:{opt shi:fts(#)}} The number of shifts of the Quasi-Monte Carlo integration algorithm to use. Must be a strictly positive integer. Defaults to 12.{p_end} {synopt:{opt sam:ples(#)}} 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.{p_end} {synopt:{opt alp:ha(#)}} The value of the Monte Carlo confidence factor to use. Must be strictly positive. Defaults to 3.{p_end} {synoptline} {p2colreset}{...} {p 4 6 2} {marker description}{...} {title:Description} {pstd} {cmd:mvnormal} computes the distribution function of the multivariate normal distribution for arbitrary limits, mean vectors and correlation matrices. {marker options}{...} {title:Options} {dlgtab:Main} {phang} {opt low:er(numlist miss)} The vector of lower limits of length k. Use . to indicate a value is -Infinity. {phang} {opt upp:er(numlist miss)} The vector of upper limits of length k. Use . to indicate a value is +Infinity. {phang} {opt me:an(numlist)} The mean vector of length k. No missing values allowed. {phang} {opt s:igma(string)} The covariance matrix of dimension k. Must be symmetric positive-definite. {phang} {opt shi:fts(#)} The number of shifts of the Quasi-Monte Carlo integration algorithm to use. Must be a strictly positive integer. Defaults to 12. {phang} {opt sam:ples(#)} 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. {phang} {opt alp:ha(#)} The value of the Monte Carlo confidence factor to use. Must be strictly positive. Defaults to 3. {marker examples}{...} {title:Examples} {phang} {stata mat Sigma = (1, 0.5, 0.5 \ 0.5, 1, 0.5 \ 0.5, 0.5, 1)} {phang} {stata mvnormal, lower(-2.06, -2.06, -2.06) upper(2.06, 2.06, 2.06) mean(0, 0, 0) sigma(Sigma)} {title:Authors} {p} Michael J. Grayling & Adrian P. Mander, MRC Biostatistics Unit, Cambridge, UK. Email {browse "mjg211@cam.ac.uk":mjg211@cam.ac.uk} {title: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: {help mvnormalden} (if installed) {help rmvnormal} (if installed) {help invmvnormal} (if installed)