{smcl} {* *! version 1.1 24jul2017} {cmd:help mata mvnxpb()} {hline} {title:Title} {p 4 8 2} {bf:mvnxpb()} {hline 2} Approximate computation of multivariate normal probabilities using bivariate conditioning (Genz and Trinh, 2016) {title:Syntax} {p 8 12 2} {it:real scalar}{bind: } {cmd:mvnxpb(}{it:real column vector ub, real column vector m, real matrix V}{cmd:)} {p 8 12 2} {it:real colvector}{bind: } {cmd:mvnxpb(}{it:real column vector ub, real column vector m, real matrix V, "dfdx"}{cmd:)} {title:Description} {p 4 4 2} {cmd:mvnxpb(}{it:ub, m, V}{cmd:)} returns a real scalar containing the approximated value of the multivariate normal (MVN) distribution with means {it:m}, variance-covariance {it:V} and upper integration limits {it:ub}. {p 4 4 2} {cmd:mvnxpb(}{it:ub, m, V, "dfdx"}{cmd:)} returns a vector of the same dimension as {it:m} containing the first-order derivatives of the approximated probability with respect to {it:x = ub - m}. {title:Conformability} {p 4 4 2} {cmd:mvnxpb(}{it:ub, m, V}{cmd:)}: {p_end} {it:ub}: {it:n x} 1 {it:m}: {it:n x} 1 {it:V}: {it:n x n} {it:result}: {it: 1 x} 1 {p 4 4 2} {cmd:mvnxpb(}{it:ub, m, V, "dfdx"}{cmd:)}: {p_end} {it:ub}: {it:n x} 1 {it:m}: {it:n x} 1 {it:V}: {it:n x n} {it:"dfdx"}: {it: string} {it:result}: {it:n x} 1 {title:Author} We would like to thank Alan Genz for giving us the permission of redistribute the Mata-translated version of his Matlab function mvnxpb(). Svetlana Mladenovic, FAO svetlana.mladenovic@fao.org Federico Belotti Department of Economics and Finance University of Rome Tor Vergata federico.belotti@uniroma2.it {title:References} {pstd} Genz, A., and Trinh, G., (2016), "Numerical Computation of Multivariate Normal Probabilities Using Bivariate Conditioning", Monte Carlo and Quasi-Monte Carlo Methods, edited by Cools R. and Nuyens D., Springer International Publishing, p.289-302. {title:Also see} {p 4 13 2} {space 2}Help: {bf:{help mf_ghk: ghk()}} {p_end}