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.
Publié le : 1997-11-14
Classification:
extreme values,
Poisson distribution,
large deviations,
triangular arrays,
regular variation,
subexponential distributions,
modelling of extremes,
radiation counts,
60G70,
60F10
@article{1043862420,
author = {Anderson, Clive W. and Coles, Stuart G. and H\"usler, J\"urg},
title = {Maxima of Poisson-like variables and related triangular
arrays},
journal = {Ann. Appl. Probab.},
volume = {7},
number = {1},
year = {1997},
pages = { 953-971},
language = {en},
url = {http://dml.mathdoc.fr/item/1043862420}
}
Anderson, Clive W.; Coles, Stuart G.; Hüsler, Jürg. Maxima of Poisson-like variables and related triangular
arrays. Ann. Appl. Probab., Tome 7 (1997) no. 1, pp. 953-971. http://gdmltest.u-ga.fr/item/1043862420/