Testing the Gumbel hypothesis via the Pot-method
type: Item
instance of: scholarly article
title: Testing the Gumbel hypothesis via the Pot-method
zbMATH Open document ID: 0923.62050
DOI: 10.1023/A:1009910806693
author: Frank Marohn
published in: Extremes
publication date: 1999-09-14T00:00:00Z
review text: The hypothesis \(H_0\) is tested that the distribution function \(F\) of an i.i.d. sample \(X_1\),\dots, \(X_n\) belongs to the extremal domain of attraction of the Gumbel distribution \(G_0(x)=\exp(-e^{-x})\). The alternative is that \(F\) belongs to the domain of attraction of the Fréchet or the Weibull distribution. The test is based on the point process \(N_{n,t_n}\) of the exceedances over a given threshold \(t_n\). Local asymptotic normality of the \(H_0\) testing problem by \(N_{n,t_n}\) with local alternatives is demonstrated in the case when \(t_n\to\infty\), but not too fast. The asymptotically optimal test sequence of fixed level \(\alpha\) for the two-sided testing problem is constructed and its asymptotic power function is evaluated. Simulation results are presented.
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 60G70
zbMATH DE Number: 1336671
zbMATH Keywords: Gumbel distribution
zbMATH Keywords: local alternatives
zbMATH Keywords: local asymptotic normality
zbMATH Keywords: exceedances over threshold
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1336671