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Editor: Universidad Carlos III de Madrid. Departamento de Estadística

Issued date: 2007-07

Serie-No.: UC3M Working papers. Statistics and Econometrics07-14

Keywords: Goodness-of-fit , Exponentiality , Maximum correlation , Decomposition of tests statistics , Exact distribution , L-statistics , 62G10 , 62G30 , 62E15

Rights: Atribución-NoComercial-SinDerivadas 3.0 España

Abstract:In Fortiana and Grané (2002) we study a scale-free statistic, based on Hoeffdings maximumcorrelation, for testing exponentiality. This statistic admits an expansion along a countable set oforthogonal axes, originating a sequence of statistics. Linear combIn Fortiana and Grané (2002) we study a scale-free statistic, based on Hoeffdings maximumcorrelation, for testing exponentiality. This statistic admits an expansion along a countable set oforthogonal axes, originating a sequence of statistics. Linear combinations of a given number p ofterms in this sequence can be written as a quotient of L-statistics. In this paper we propose a scalefreeadaptive statistic for testing exponentiality with optimal power against a specific alternative.We obtain its exact distribution and compare it with other scale-free statistics for testingexponentiality, such as the Stephens modification of the Shapiro-Wilk statistic, the Gini statisticand the Qn statistic defined in Fortiana and Grané (2002).+-





Author: Grané, Aurea; Fortiana, Josep

Source: http://e-archivo.uc3m.es


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Universidad Carlos III de Madrid Repositorio institucional e-Archivo http:--e-archivo.uc3m.es Departamento de Estadística DES - Working Papers.
Statistics and Econometrics.
WS 2007-07 A scale-free adaptive statistic for testing exponentiality against Weibull and generalized Pareto distributions Grané, Aurea http:--hdl.handle.net-10016-858 Descargado de e-Archivo, repositorio institucional de la Universidad Carlos III de Madrid Working Paper 07-56 Statistic and Econometric Series 14 July 2007 Departamento de Estadística Universidad Carlos III de Madrid Calle Madrid, 126 28903 Getafe (Spain) Fax (34-91) 6249849 A SCALE-FREE ADAPTIVE STATISTIC FOR TESTING EXPONENTIALITY AGAINST WEIBULL AND GENERALIZED PARETO DISTRIBUTIONS ∗ Aurea Grané1 and Josep Fortiana 2 Abstract In Fortiana and Grané (2002) we study a scale-free statistic, based on Hoeffdings maximum correlation, for testing exponentiality.
This statistic admits an expansion along a countable set of orthogonal axes, originating a sequence of statistics.
Linear combinations of a given number p of terms in this sequence can be written as a quotient of L-statistics.
In this paper we propose a scalefree adaptive statistic for testing exponentiality with optimal power against a specific alternative. We obtain its exact distribution and compare it with other scale-free statistics for testing exponentiality, such as the Stephens modification of the Shapiro-Wilk statistic, the Gini statistic and the Qn statistic defined in Fortiana and Grané (2002). Keywords: Goodness-of-fit, exponentiality, maximum correlation, decomposition of tests statistics, exact distribution, L-statistics. AMS subject classification: 62G10, 62G30, 62E15. ∗ 1 Statistics Department, Universidad Carlos III de Madrid, C- Madrid 126, 28903 Getafe (Madrid), Spain, e-mail: agrane@est-econ.uc3m.es Corresponding author. 2 Dept.
de Probabilitat, Lògica i Estadística, Universitat de Barcelona, C- Gran Via de les Corts Catalanes, 585,...





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