A scale-free adaptive statistic for testing exponentiality against Weibull and generalized Pareto distributions

Josep Fortiana

DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística

Abstract: In Fortiana and Grané (2002) we study a scale-free statistic, based on Hoeffding's 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: 62E15; Exact; distribution; Goodness-of-fit; Exponentiality; Maximum; correlation; Decomposition; of; tests; statistics; L-statistics; 62G10; 62G30 (search for similar items in EconPapers)
Date: 2007-07
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Persistent link: https://EconPapers.repec.org/RePEc:cte:wsrepe:ws075614

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