We propose a method to approximate a class of exponential multivariate integrals using moment relaxations. Using this approach, both lower and upper bounds of the integrals are obtained and we show that these bound values asymptotically converge to the real value of the integrals when the moment degree r increases. We further demonstrate the method by calculating both hypercubic and order statistic probabilities for multivariate normal distributions.
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January 2007
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View Multivariate exponential integral approximations: a moment approach