MAXIMA OF POISSON-LIKE VARIABLES AND RELATED TRIANGULAR ARRAYS

被引：25

作者：

Anderson, Clive W. ^{[1
]}

Coles, Stuart G. ^{[2
]}

Husler, Jurg ^{[3
]}

机构：

[1] Univ Sheffield, Sch Math & Stat, Sheffield S3 7RH, S Yorkshire, England

[2] Univ Lancaster, Dept Math & Stat, Lancaster LA1 4YF, England

[3] Univ Bern, Inst Math Stat & Versicherungslehre, CH-3012 Bern, Switzerland

来源：

ANNALS OF APPLIED PROBABILITY | 1997年 / 7卷 / 04期

关键词：

extreme values; Poisson distribution; large deviations; triangular arrays; regular variation; subexponential distributions; modelling of extremes; radiation counts;

D O I：

10.1214/aoap/1043862420

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

It is known that maxima of independent Poisson variables cannot be normalized to converge to a nondegenerate limit distribution. On the other hand, the Normal distribution approximates the Poisson distribution for large values of the Poisson mean, and maxima of random samples of Normal variables may be linearly scaled to converge to a classical extreme value distribution. We here explore the boundary between these two kinds of behavior. Motivation comes from the wish to construct models for the statistical analysis of extremes of background gamma radiation over the United Kingdom. The methods extend to row-wise maxima of certain triangular arrays, for which limiting distributions are also derived.

引用

页码：953 / 971

页数：19

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