{smcl}
{* *! version 1.1  24jul2017}
{cmd:help mata mvnxpb()}
{hline}

{title:Title}

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{bf:mvnxpb()} {hline 2} Approximate computation of multivariate normal probabilities using bivariate conditioning (Genz and Trinh, 2016)


{title:Syntax}

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{it:real scalar}{bind:    }
{cmd:mvnxpb(}{it:real column vector ub, real column vector m, real matrix V}{cmd:)}

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{it:real colvector}{bind:    }
{cmd:mvnxpb(}{it:real column vector ub, real column vector m, real matrix V, "dfdx"}{cmd:)}


{title:Description}

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{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}

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{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}

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{space 2}Help:   
{bf:{help mf_ghk: ghk()}}
{p_end}