E‐Bayesian and hierarchical Bayesian estimations for parallel system model in the presence of masked data

Cai, Jing; Shi, Yimin; Lin, Ting Hsiang

doi:10.1002/cpe.5615

Cited by 2 publications

(1 citation statement)

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“…Han [15] derived the E-B and HB estimations of the shape parameter of Pareto distribution. For more details about E-Bayesian estimation (E-BE), we may refer to [16][17][18][19]. However, those authors used hierarchical prior density function.…”

Section: Introductionmentioning

confidence: 99%

E-Bayesian Estimation of Hierarchical Poisson-Gamma Model on the Basis of Restricted and Unrestricted Parameter Spaces

et al. 2023

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In this study, we use the idea of the hierarchical model (HM) to estimate an unknown parameter of the hierarchical Poisson-Gamma model using the E-Bayesian (E-B) theory. We propose the idea of hierarchical probability function instead of the traditional hierarchical prior density function. We aim to infer E-B estimates with respect to the conjugate Gamma prior distribution along with the E-posterior risks on the basis of different symmetric and asymmetric loss functions (LFs) under restricted and unrestricted parameter spaces using uniform hyperprior. Whereas, E-B estimators are compared with maximum likelihood estimators (MLEs) using mean squared error (MSE). Monte Carlo simulations are prosecuted to study the efficiency of E-B estimators empirically. It is shown that the LFs under a restricted parameter space dominate to estimate the parameter of the hierarchical Poisson-Gamma model. It is also found that the E-B estimators are more precise than MLEs, and Stein’s LF has the least E-PR. Moreover, the application of outcomes to a real-life example has been made for analysis, comparison, and motivation.

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