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New tests for exponentiality against new better than used in th quantile

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  • Paul Janssen
  • Jan Swanepoel
  • Noël Veraverbeke

Abstract

A new characterisation of the exponential distribution in a wide class of new better than used in pth quantile (NBUp) lifetime distributions is presented. This leads to new classes of scale-free goodness-of-fit tests for exponentiality against NBUp alternatives. The limiting distributions of the test statistics under the null and alternative hypotheses are derived and the tests are shown to be consistent against NBUp alternatives. Pitman efficacies are calculated and a limited Monte Carlo study is conducted to compare the tests with regard to power for small and moderate sample sizes against a range of alternative distributions. On the basis of overall good performance and ease of computation, a member of the class of test statistics which is based on the sample Winsorised mean is recommended as a scale-free goodness-of-fit test for the exponential distribution.

Suggested Citation

  • Paul Janssen & Jan Swanepoel & Noël Veraverbeke, 2009. "New tests for exponentiality against new better than used in th quantile," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(1), pages 85-97.
    • Handle: RePEc:taf:gnstxx:v:21:y:2009:i:1:p:85-97
    DOI: 10.1080/10485250802454953
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    References listed on IDEAS

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    1. Harry Joe & Frank Proschan, 1984. "Percentile Residual Life Functions," Operations Research, INFORMS, vol. 32(3), pages 668-678, June.
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