Dispersion Models for Extremes

Details Dispersion Models for Extremes Dispersion Models for Extremes

2007-12-28

arxiv.org/abs/0712.4323v1

Mathematics

Statistics Theory

23 pages. Abstract submitted to the 56th Session of the ISI, Lisboa, 2007

Scientific paper

We propose extreme value analogues of natural exponential families and exponential dispersion models, and introduce the slope function as an analogue of the variance function. The set of quadratic and power slope functions characterize well-known families such as the Rayleigh, Gumbel, power, Pareto, logistic, negative exponential, Weibull and Fr\'echet. We show a convergence theorem for slope functions, by which we may express the classical extreme value convergence results in terms of asymptotics for extreme dispersion models. The main idea is to explore the parallels between location families and natural exponential families, and between the convolution and minimum operations.

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