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

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  • Grané, Aurea
  • Fortiana, Josep

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).

Suggested Citation

  • Grané, Aurea & Fortiana, Josep, 2007. "A scale-free adaptive statistic for testing exponentiality against Weibull and generalized Pareto distributions," DES - Working Papers. Statistics and Econometrics. WS ws075614, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws075614
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    62E15;

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