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

Abstract:

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 longrun 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
