Evaluating Nearly Singular Multinormal Expectations with Application to Wave Distributions |
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Authors: | Per A Brodtkorb |
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Institution: | (1) FFI, PO Box 115, NO-3191 Horten, Norway |
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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 long-run distributions of Gaussian wave characteristics, a difficult problem where previous algorithms fail to
compute accurate values in reasonable time.
AMS 2000 Subject Classification 65C60, 65D15, 68W25 |
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Keywords: | Multivariate normal probabilities Singular distribution Wave crest amplitude and crest velocity Numerical integration |
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