Goodness-of-fit tests for the Cauchy distribution
type: Item
instance of: scholarly article
title: Goodness-of-fit tests for the Cauchy distribution
zbMATH Open document ID: 1007.62044
author: Bora H. Onen
author: Dennis C. Dietz
author: Vincent C. Yen
author: Albert H. Moore
published in: Computational Statistics
publication date: 2003-03-09T00:00:00Z
review text: The Cauchy family of distributions is defined by the pdf \[ f(x)=[\pi\psi(1+(x-\lambda)\psi^{-1})]^{-2}, \] where \(\lambda\) and \(\psi\) are the location and scale parameters. The authors consider different estimators for \(\psi\) and \(\lambda\) (including an iterative MLE algorithm) and five goodness-of-fit tests for this family: Kolmogorov, Kuiper, Cramér-von-Mises, Watson and Anderson-Darling. Symmetrization around the location parameter is proposed to derive more powerful tests. The critical values are derived for the tests via Monte-Carlo. The power of the tests is compared also via simulations. The conclusion is that the Kuiper test is most powerful against almost all alternative distributions (\(t\)-family, normal, beta, Weibull).
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 65C05
zbMATH DE Number: 1878601
zbMATH Keywords: Kolmogorov test
zbMATH Keywords: Kuiper test
zbMATH Keywords: Cramer-von-Mises test
zbMATH Keywords: Watson test
zbMATH Keywords: Anderson-Darling test
MaRDI profile type: Publication
full work available at URL: s001800100053
OpenAlex ID: W1999595879
DOI: 10.1007/S001800100053
description: scientific article; zbMATH DE number 1878601