Numerical Evaluation of Multinormal Probabilities
Per A. Brodtkorb
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2004
ISSN 14039338

Abstract:

The multivariate normal probability integral with a product correlation structure
can be transformed to a one dimensional integral and easily evaluated when
the correlation matrix is nonsingular and well conditioned. However, the
nearly singular case is much more difficult and previous methods fail to
compute it with high numerical precision. This paper demonstrates that the
(nearly) singular case can be computed to almost double precision using a
three step adaptive Simpson method with the epsilonalgorithm by Wynn (1956).
Tests using randomly chosen problems show that the method gives more reliable
results than the adaptive Simpson method of Dunnett (1989) as well as the
globally adaptive integration routine DQAGPE from QUADPACK

(Piessens et al., 1983).



Key words:

multivariate normal probabilities, singular distribution, product correlation
structure, numerical integration,

statistical computation
