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Tests for exponentiality against theM andLM-Classes of life distributions

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Abstract

This paper studies tests for exponentiality against the nonparametric classesM andLM of life distributions introduced by Klar and Müller (2003). The test statistics are integrals of the difference between the empirical moment generating function of given data and the moment generating function of a fitted exponential distribution. We derive the limit distributions of the test statistics in case of a general underlying distribution and the local approximate Bahadur efficiency of the procedures against several parametric families of alternatives to exponentiality. The finite sample behavior of the tests is examined by means of a simulation study. Finally, the tests under discussion are applied to two data sets, and we discuss the applicability of the tests under random censorship.

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Authors and Affiliations

  1. Institut für Mathematische Stochastik, Universität Karlsruhe, Englerstr 2, 76128, Karlsruhe, Germany

    Bernhard Klar

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  1. Bernhard Klar
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Correspondence to Bernhard Klar.

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Klar, B. Tests for exponentiality against theM andLM-Classes of life distributions. TEST 14, 543–565 (2005). https://doi.org/10.1007/BF02595417

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  • DOI: https://doi.org/10.1007/BF02595417

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