Goodness-of-fit testing for Weibull-type behavior |
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Authors: | Yuri Goegebeur Armelle Guillou |
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Institution: | 1. Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark;2. Institut de Recherche Mathématique Avancée UMR 7501, Université de Strasbourg et CNRS, 7 rue René-Descartes, 67084 Strasbourg cedex, France |
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Abstract: | In the process of analyzing data, testing the fit of a model under consideration is a prerequisite for performing inference about the model parameters. In this paper we examine the goodness-of-fit testing problem for assessing whether a sample is consistent with the Weibull-type model. Inspired by the Jackson and the Lewis test statistics, originally proposed as goodness-of-fit tests for the exponential distribution, we introduce two new statistics for testing Weibull-type behavior, and study their asymptotic properties. Moreover, given that the statistics are ratios of estimators for the Weibull-tail coefficient, we obtain new estimators for the latter, and establish their consistency and asymptotic normality. The small sample behavior of our statistics and estimators is evaluated on the basis of a simulation study. |
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Keywords: | Extreme value statistics Weibull-type model Weibull-tail coefficient Goodness-of-fit |
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