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A saddlepoint approximation for testing exponentiality against some increasing failure rate alternatives

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  • Gatto, Riccardo
  • Jammalamadaka, S. Rao
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    Abstract

    In this article we discuss uniformly most powerful unbiased tests for testing exponentiality against a specific class of two-parameter exponential models with increasing failure rate. We show that the optimal test statistic for this problem admits an alternative representation in terms of a spacings statistic. Using the conditional saddlepoint approximation proposed by Gatto and Jammalamadaka (J. Amer. Statist. Assoc. 94 (1999) 533), we provide highly accurate approximations for the significance values. The test procedure is illustrated with two practical examples from reliability and survival analysis. We also obtain the asymptotic distribution of the test statistic under a sequence of converging alternatives, which allows for the computation of asymptotic relative efficiency.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 58 (2002)
    Issue (Month): 1 (May)
    Pages: 71-81

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    Handle: RePEc:eee:stapro:v:58:y:2002:i:1:p:71-81

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    Keywords: Exponential distribution Goodness-of-fit test Reliability analysis Spacings statistics Survival analysis Uniform spacings;

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    1. Wang, Suojin, 1995. "One-step saddlepoint approximations for quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 20(1), pages 65-74, July.
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