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1976•Communication in Statistics- Theory and MethodsRequires access

Inequalities for tail probabilities for the multivariate normal distribution

W. L. Harkness, Ashok V. Godambe

Open publisher page 4 citations

Abstract

Inequalities for tail probabilities of the multivariate normal distribution are obtained, as a generalization of those given by Feller (1966). Upper and lower bounds are given in the equi-correlated case. For an arbitrary correlation matrix R, an upper bound is obtained, using a result of Slepian (1962) which asserts that certain multivariate normal probabilities are a non-decreasing function of correlations.

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What this paper is about

Inequalities for tail probabilities of the multivariate normal distribution are obtained, as a generalization of those given by Feller (1966). Upper and lower bounds are given in the equi-correlated case. For an arbitrary correlation matrix R, an upper bound is obtained, using a result of Slepian (1962) which asserts that certain multivariate normal probabilities are a non-decreasing function of correlations.

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Available abstract

Inequalities for tail probabilities of the multivariate normal distribution are obtained, as a generalization of those given by Feller (1966). Upper and lower bounds are given in the equi-correlated case. For an arbitrary correlation matrix R, an upper bound is obtained, using a result of Slepian (1962) which asserts that certain multivariate normal probabilities are a non-decreasing function of correlations.

Key concepts: Normal-Wishart distribution, Multivariate statistics, Matrix t-distribution, Multivariate normal distribution, Matrix normal distribution, Mathematics, Inverse-Wishart distribution, Multivariate stable distribution

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