Dispersion models for extremes |
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Authors: | Bent Jørgensen Yuri Goegebeur José Raúl Martínez |
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Institution: | 1.Department of Mathematics and Computer Science,University of Southern Denmark,Odense M,Denmark;2.FAMAF,Universidad Nacional de Córdoba,Córdoba,Argentina |
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Abstract: | 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. A class of extreme generalized linear regression models for analysis of
extremes and lifetime data is introduced. The set of quadratic and power slope functions characterize well-known families
such as the Rayleigh, Gumbel, power, Pareto, logistic, negative exponential, Weibull and Fréchet. 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 key idea is to explore the parallels between location families and natural exponential families, and
between the convolution and minimum operations. |
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Keywords: | |
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