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

Author

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  • Hüsler, Jürg
  • Liu, Regina Y.
  • Singh, Kesar

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.

Suggested Citation

  • Hüsler, Jürg & Liu, Regina Y. & Singh, Kesar, 2002. "A Formula for the Tail Probability of a Multivariate Normal Distribution and Its Applications," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 422-430, August.
    • Handle: RePEc:eee:jmvana:v:82:y:2002:i:2:p:422-430
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    Cited by:

    1. Hashorva, Enkelejd, 2010. "Asymptotics of the norm of elliptical random vectors," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 926-935, April.
    2. Das, Bikramjit & Engelke, Sebastian & Hashorva, Enkelejd, 2015. "Extremal behavior of squared Bessel processes attracted by the Brown–Resnick process," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 780-796.

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