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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

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.

Suggested Citation

  • Gatto, Riccardo & Jammalamadaka, S. Rao, 2002. "A saddlepoint approximation for testing exponentiality against some increasing failure rate alternatives," Statistics & Probability Letters, Elsevier, vol. 58(1), pages 71-81, May.
    • Handle: RePEc:eee:stapro:v:58:y:2002:i:1:p:71-81
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    References listed on IDEAS

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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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    Cited by:

    1. Montebruno, Piero & Bennett, Robert J. & van Lieshout, Carry & Smith, Harry, 2019. "A tale of two tails: Do Power Law and Lognormal models fit firm-size distributions in the mid-Victorian era?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 858-875.
    2. Sreenivasa Rao Jammalamadaka & Emanuele Taufer, 2002. "The use of Mean Residual Life in testing departures from Esxponentiality," Quaderni DISA 071, Department of Computer and Management Sciences, University of Trento, Italy, revised 12 Sep 2003.
    3. Riccardo Gatto, 2019. "Saddlepoint Approximation for Data in Simplices: A Review with New Applications," Stats, MDPI, vol. 2(1), pages 1-27, February.

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