Publication: A scale-free adaptive statistic for testing exponentiality against Weibull and generalized Pareto distributions
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2007-07
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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).
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Goodness-of-fit, Exponentiality, Maximum correlation, Decomposition of tests statistics, Exact distribution, L-statistics, 62G10, 62G30, 62E15