*! version 1.1 24jul2017

help mata mvnxpb()

Title

mvnxpb() -- Approximate computation of multivariate normal probabilities using bivariate conditioning (Genz and Trinh, 2016)

Syntax

real scalar
mvnxpb(real column vector ub, real column vector m, real matrix V)

real colvector
mvnxpb(real column vector ub, real column vector m, real matrix V, "dfdx")

Description

mvnxpb(ub, m, V) returns a real scalar containing the approximated value of the multivariate normal (MVN) distribution with means m, variance-covariance V and upper integration limits ub.

mvnxpb(ub, m, V, "dfdx") returns a vector of the same dimension as
m containing the first-order derivatives of the approximated probability with respect to x = ub - m.

Conformability

mvnxpb(ub, m, V):

ub: n x 1
m: n x 1
V: n x n
result: 1 x 1

mvnxpb(ub, m, V, "dfdx"):

ub: n x 1
m: n x 1
V: n x n
"dfdx": string
result: n x 1

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

References

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.

Also see

Help:
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