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Likelihood and Bayesian estimation of \(P(Y{<}X)\) using lower record values from a proportional reversed hazard family

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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.

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Authors and Affiliations

  1. Department of Economics, Statistics and Finance, University of Calabria, Via Pietro Bucci, Cubo 0C, 87036, Arcavacata di Rende, CS, Italy

    Francesca Condino, Filippo Domma & Giovanni Latorre

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  1. Francesca Condino
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  2. Filippo Domma
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  3. Giovanni Latorre
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Correspondence to Francesca Condino.

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Condino, F., Domma, F. & Latorre, G. Likelihood and Bayesian estimation of \(P(Y{<}X)\) using lower record values from a proportional reversed hazard family. Stat Papers 59, 467–485 (2018). https://doi.org/10.1007/s00362-016-0772-9

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  • DOI: https://doi.org/10.1007/s00362-016-0772-9

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