The E-Bayesian and hierarchical Bayesian estimations for the proportional reversed hazard rate model based on record values. (English) Zbl 07192061
Summary: In this paper, E-Bayesian and hierarchical Bayesian estimations of the shape parameter, when the underlying distribution belongs to the proportional reversed hazard rate model, are considered. Maximum likelihood, Bayesian and E-Bayesian estimates of the unknown parameter and reliability function are obtained based on record values. The Bayesian estimates are derived based on squared error and linear-exponential loss functions. It is pointed out that some previously obtained order relations of E-Bayesian estimates are inadequate and these results are improved. The relationship between E-Bayesian and hierarchical Bayesian estimations is obtained under the same loss functions. The comparison of the derived estimates is carried out by using Monte Carlo simulations. A real data set is analysed for an illustration of the findings.
Keywords:
E-Bayesian estimation; hierarchical Bayesian estimation; record values; proportional reversed hazard rate model; inverse Weibull distributionReferences:
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