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Multivariate normal cumulative distribution (QMC)

version (9.85 KB) by Zdravko Botev
state-of-the-art algorithm for computing the multivariate normal cdf in medium dimensions


Updated 28 Oct 2015

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Computes the probability Pr(l<X<u), where 'X' is a zero-mean multivariate normal vector with covariance 'Sig'.
In medimum to high dimensions using Quasi Monte Carlo. This algorithm is superior to the one in Matlab's statistics toolbox, see example.
Reference: Z. I. Botev (2015), "The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting", submitted to JRSS(B)

Cite As

Zdravko Botev (2022). Multivariate normal cumulative distribution (QMC) (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2015b
Compatible with any release
Platform Compatibility
Windows macOS Linux

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