A Formula for the Tail Probability of a Multivariate Normal Distribution and Its Applications

Jürg Hüsler, Regina Y. Liu and Kesar Singh

Journal of Multivariate Analysis, 2002, vol. 82, issue 2, 422-430

Abstract: An exact asymptotic formula for the tail probability of a multivariate normal distribution is derived. This formula is applied to establish two asymptotic results for the maximum deviation from the mean: the weak convergence to the Gumbel distribution of a normalized maximum deviation and the precise almost sure rate of growth of the maximum deviation. The latter result gives rise to a diagnostic tool for checking multivariate normality by a simple graph in the plane. Some simulation results are presented.

Keywords: multivariate; normal; distribution; tail; probability; Gumbel; distribution; maximum; deviation; growth; rate; sum; of; [chi]2; random; variables (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (2)

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