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

✍ Scribed by Jürg Hüsler; Regina Y. Liu; Kesar Singh

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
113 KB
Volume
82
Category
Article
ISSN
0047-259X

No coin nor oath required. For personal study only.

✦ Synopsis

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.

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