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Change-point analysis with bathtub shape for the exponential distribution

Author

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  • Xia Cai
  • Khamis Khalid Said
  • Wei Ning

Abstract

Likelihood ratio type test statistic and Schwarz information criterion statistics are proposed for detecting possible bathtub-shaped changes in the parameter in a sequence of exponential distributions. The asymptotic distribution of likelihood ratio type statistic under the null hypothesis and the testing procedure based on Schwarz information criterion are derived. Numerical critical values and powers of two methods are tabulated for certain selected values of the parameters. The tests are applied to detect the change points for the predator data and Stanford heart transplant data.

Suggested Citation

  • Xia Cai & Khamis Khalid Said & Wei Ning, 2016. "Change-point analysis with bathtub shape for the exponential distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(15), pages 2740-2750, November.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:15:p:2740-2750
    DOI: 10.1080/02664763.2016.1143455
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    References listed on IDEAS

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    1. Haccou, Patsy & Meelis, Evert & van de Geer, Sara, 1987. "The likelihood ratio test for the change point problem for exponentially distributed random variables," Stochastic Processes and their Applications, Elsevier, vol. 27, pages 121-139.
    2. Ashish Sen & S. Srivastava, 1975. "On tests for detecting change in mean when variance is unknown," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 27(1), pages 479-486, December.
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    Cited by:

    1. Mei Li & Wei Ning & Yubin Tian, 2024. "Change Point Test for Length-Biased Lognormal Distribution under Random Right Censoring," Mathematics, MDPI, vol. 12(11), pages 1-20, June.
    2. Cai, Xia & Tian, Yubin & Ning, Wei, 2017. "Modified information approach for detecting change points in piecewise linear failure rate function," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 130-140.
    3. Weizhong Tian & Liyuan Pang & Chengliang Tian & Wei Ning, 2023. "Change Point Analysis for Kumaraswamy Distribution," Mathematics, MDPI, vol. 11(3), pages 1-22, January.

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