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The E-Bayesian and hierarchical Bayesian estimations for the proportional reversed hazard rate model based on record values

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ABSTRACT 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… Click to show full abstract

ABSTRACT 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: hierarchical bayesian; bayesian hierarchical; proportional reversed; hazard rate; reversed hazard; bayesian estimations

Journal Title: Journal of Statistical Computation and Simulation
Year Published: 2017

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