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Tests of non-monotonic stochastic aging notions in reliability theory

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  • M. Anis

Abstract

Testing of various classes of life distributions has been a subject of investigation for more than four decades. In this study we restrict ourselves to the problem of testing exponentiality against non-monotonic aging notions. We model non-monotonic aging using the notions of bathtub failure rate, increasing and then decreasing mean residual life and new worse then better than used in expectation classes. The different tests of exponentiality against these alternatives are discussed in detail. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • M. Anis, 2014. "Tests of non-monotonic stochastic aging notions in reliability theory," Statistical Papers, Springer, vol. 55(3), pages 691-714, August.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:3:p:691-714
    DOI: 10.1007/s00362-013-0520-3
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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. Murari Mitra & Sujit Basu, 1995. "Change point estimation in non-monotonic aging models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 483-491, September.
    3. 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. 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.
    2. Ruhul Ali Khan & Dhrubasish Bhattacharyya & Murari Mitra, 2021. "Exact and asymptotic tests of exponentiality against nonmonotonic mean time to failure type alternatives," Statistical Papers, Springer, vol. 62(6), pages 3015-3045, December.
    3. Priyanka Majumder & Murari Mitra, 2021. "Detecting trend change in hazard functions—an L-statistic approach," Statistical Papers, Springer, vol. 62(1), pages 31-52, February.

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    More about this item

    Keywords

    Change point; Empirical distribution function; Gaussian process; Total time on test; 62 G10; 62 G20; 90 B25;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G20 - Financial Economics - - Financial Institutions and Services - - - General
    • B25 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Historical; Institutional; Evolutionary; Austrian; Stockholm School

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