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November 1997 Maxima of Poisson-like variables and related triangular arrays
Clive W. Anderson, Stuart G. Coles, Jürg Hüsler
Ann. Appl. Probab. 7(4): 953-971 (November 1997). DOI: 10.1214/aoap/1043862420

Abstract

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.

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Clive W. Anderson. Stuart G. Coles. Jürg Hüsler. "Maxima of Poisson-like variables and related triangular arrays." Ann. Appl. Probab. 7 (4) 953 - 971, November 1997. https://doi.org/10.1214/aoap/1043862420

Information

Published: November 1997
First available in Project Euclid: 29 January 2003

zbMATH: 0897.60052
MathSciNet: MR1484793
Digital Object Identifier: 10.1214/aoap/1043862420

Subjects:
Primary: 60G70
Secondary: 60F10

Keywords: Extreme values , large deviations , modelling of extremes , Poisson distribution , radiation counts , regular variation , Subexponential distributions , triangular arrays

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.7 • No. 4 • November 1997
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