Recent and classical tests for exponentiality: a partial review with comparisons
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A wide selection of classical and recent tests for exponentiality are discussed and compared. The classical procedures include the statistics of Kolmogorov-Smirnov and Cramér-von Mises, a statistic based on spacings, and a method involving the score function. Among the most recent approaches emphasized are methods based on the empirical Laplace transform and the empirical characteristic function, a method based on entropy as well as tests of the Kolmogorov-Smirnov and Cramér-von Mises type that utilize a characterization of exponentiality via the mean residual life function. We also propose a new goodness-of-fit test utilizing a novel characterization of the exponential distribution through its characteristic function. The finite-sample performance of the tests is investigated in an extensive simulation study.
AMS 1991 Classification Numbers:62G10 62G20
KeywordsGoodness-of-fit test exponential distribution empirical characteristic function empirical distribution function integrated empirical distribution function empirical Laplace transform entropy mean residual life function
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Research on this topic started while the first author was visiting the University of Patras. Norbert Henze would like to thank the Department of Engineering Sciences for its hospitality and strong support. The authors are grateful to the referees for many constructive comments.