This book covers the computation of probabilities associated with the multivariate normal and multivariate t distributions. The challenge lies in the multivariate aspect of these computations, which are clearly nontrivial. For example, how does one evaluate numerically the cumulative distribution function of a trivariate normal random vector? Statisticians are used to computing probabilities related to the univariate normal distribution on a calculator or computer, or from tabulated entries in the back of a statistics textbook. But how does one compute similar probabilities for multivariate normal or multivariate / distributions? This book synthesizes many results published in statistics journals in recent years on this topic and provides a unique source of information on the computation of these probabilities, which arise very naturally for statistical inference in many modern applications. I believe that it fills a gap in the literature on multivariate statistics.
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