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A Hollander–Proschan type test when ageing is not monotone

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  • Ghosh, Shyamal
  • Mitra, Murari

Abstract

We develop a class of Hollander–Proschan type tests for testing exponentiality against certain non-monotonic ageing alternatives. We derive the exact distribution of our statistics under the null hypothesis and asymptotic distributions under both null and alternative hypotheses. The test is shown to be consistent. Finally, we assess the performance of the test by means of a simulation study.

Suggested Citation

  • Ghosh, Shyamal & Mitra, Murari, 2017. "A Hollander–Proschan type test when ageing is not monotone," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 119-127.
    • Handle: RePEc:eee:stapro:v:121:y:2017:i:c:p:119-127
    DOI: 10.1016/j.spl.2016.10.015
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    References listed on IDEAS

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    1. M. Z. Anis & M. Mitra, 2005. "A simple test of exponentiality against NWBUE family of life distributions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 21(1), pages 45-53, January.
    2. Anis, M.Z. & Mitra, M., 2011. "A generalized Hollander-Proschan type test for NBUE alternatives," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 126-132, January.
    3. Anis, M.Z. & Basu, Kinjal, 2011. "The exact null distribution of the generalized Hollander-Proschan type test for NBUE alternatives," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1733-1737, November.
    4. Anis, M.Z. & Ghosh, Abhik, 2015. "Monte Carlo comparison of tests of exponentiality against NWBUE alternatives," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 115(C), pages 1-11.
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