Numerical Evaluation of Multinormal Expectations

Per A. Brodtkorb

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
The numerical computation of expectations for (nearly) singular multivariate normal distribution is a difficult problem, which frequently occurs in widely varying statistical contexts. In this article we discuss several strategies to improve the algorithm proposed by Genz and Kwong (2000) when either a moderate accuracy is requested, the correlation structure is strong, and, most importantly, the dimension of the integral is large. Test results for typical problems show an average speedup of 10 using the modified algorithm, but even more is gained as the dimension of the problem increases.
We apply the modified algorithm to compute long-run distributions of Gaussian wave characteristics, a difficult problem where previous algorithms fail to compute accurate values in reasonable time.
Key words:
multivariate normal probabilities, singular distribution, wave crest amplitude, wave crest velocity, local maxima and minima, numerical integration, statistical computation