On Testing the Exponential and Gumbel Distribution

Frank Marohn
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Frank Marohn: Katholische Universität Eichstätt, Mathematisch-Geographische Fakultät

A chapter in Extreme Value Theory and Applications, 1994, pp 159-174 from Springer

Abstract: Abstract Consider the statistical experiment (ℝ B, {H β: β ∈ ℝ }), where Hβ denotes the generalized Pareto distribution given by the von Mises parametrization and H 0 is the standard exponential distribution. We investigate the two-sided testing problem H 0 against H β, β≠0. For that testing problem an asymptotically uniformly optimal test is established. As a main tool we show that the experiment is differentiable in quadratic mean at β = 0, which is a crucial condition in the asymptotic setting. A Monte-Carlo simulation visualizes the result. Moreover, we consider the extreme value distributions G β , β ∈ ℝ, which are the most important ones in the neighborhood of the generalized Pareto distributions. We treat the testing problem Gumbel (G0) against Frechet (G β , β > 0) and Weibull (G β ,β

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-3638-9_9

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DOI: 10.1007/978-1-4613-3638-9_9

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