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Monte Carlo comparison of tests of exponentiality against NWBUE alternatives

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  • Anis, M.Z.
  • Ghosh, Abhik

Abstract

In this paper we focus on the testing of exponentiality (which essentially captures no aging) against non-monotonic aging captured by the fairly large class of new worse then better than used in expectation (NWBUE) alternatives. Three different tests are reviewed; these tests are based on three different characteristics of the NWBUE distributions, namely the moment characteristic, the scaled TTT (total time on test)-transformation and the centered form of the scaled TTT-transformation. They are compared with respect to size and power. The empirical size and empirical power of the tests are obtained by Monte Carlo simulations. The small sample critical points based on simulation are given for the “most useful” test.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:115:y:2015:i:c:p:1-11
    DOI: 10.1016/j.matcom.2015.04.004
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    References listed on IDEAS

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    1. M. Anis, 2014. "Tests of non-monotonic stochastic aging notions in reliability theory," Statistical Papers, Springer, vol. 55(3), pages 691-714, August.
    2. Saralees Nadarajah, 2009. "Bathtub-shaped failure rate functions," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(5), pages 855-863, September.
    3. 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.
    4. Belzunce, Felix & Ortega, Eva-Maria & Ruiz, Jose M., 2007. "On non-monotonic ageing properties from the Laplace transform, with actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 1-14, January.
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    Cited by:

    1. 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.

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