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Likelihood and Bayesian estimation of $$P(Y{

Author

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  • Francesca Condino

    (University of Calabria)

  • Filippo Domma

    (University of Calabria)

  • Giovanni Latorre

    (University of Calabria)

Abstract

In this paper, we study inference for the stress–strength reliability based on lower record data, where the stress and the strength variables are modeled by two independent but not identically distributed random variables from distributions belonging to the proportional reversed hazard family. Likelihood and Bayesian estimators are derived, then confidence intervals and credible sets are obtained. Moreover, we consider the Topp–Leone distribution as a particular case of distribution belonging to this family and we derive some numerical results in order to show the performance of the proposed procedures. Finally, two applications to real data are reported.

Suggested Citation

  • Francesca Condino & Filippo Domma & Giovanni Latorre, 2018. "Likelihood and Bayesian estimation of $$P(Y{," Statistical Papers, Springer, vol. 59(2), pages 467-485, June.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:2:d:10.1007_s00362-016-0772-9
    DOI: 10.1007/s00362-016-0772-9
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    References listed on IDEAS

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    4. M. E. Ghitany & S. Kotz & M. Xie, 2005. "On some reliability measures and their stochastic orderings for the Topp-Leone distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 715-722.
    5. Donatella Vicari & Johan Rene Van Dorp & Samuel Kotz, 2008. "Two-sided generalized Topp and Leone (TS-GTL) distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(10), pages 1115-1129.
    6. Saralees Nadarajah & Samuel Kotz, 2003. "Moments of some J-shaped distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(3), pages 311-317.
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