Empirical E-Bayesian estimation of hierarchical poisson and gamma model using scaled squared error loss function

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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“…. ., m)} represents the set of values drawn from the following hierarchical Poisson-Gamma model ( [20][21][22]):…”

Section: Hierarchical Poisson-gamma Modelmentioning

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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Bayesian inference on parameters and reliability characteristics for inverse Xgamma distribution under adaptive-general progressive Type-II censoring

Gangopadhyay,

Mondal,

Lodhi

et al. 2024

Journal of Radiation Research and Applied Sciences

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Statistical inference of entropy functions of generalized inverse exponential model under progressive type-II censoring test

Gong,

Yin

2024

PLoS ONE

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This article explores the estimation of Shannon entropy and Rényi entropy based on the generalized inverse exponential distribution under the condition of stepwise Type II truncated samples. Firstly, we analyze the maximum likelihood estimation and interval estimation of Shannon entropy and Rényi entropy for the generalized inverse exponential distribution. In this process, we use the bootstrap method to construct confidence intervals for Shannon entropy and Rényi entropy. Next, we select the gamma distribution as the prior distribution and apply the Lindley approximation algorithm to calculate `estimates of Shannon entropy and Rényi entropy under different loss functions including Linex loss function, entropy loss function, and DeGroot loss function respectively. Afterwards, simulation is used to calculate estimates and corresponding mean square errors of Shannon entropy and Rényi entropy in GIED model. The research results show that under DeGroot loss function, estimation accuracy of Shannon entropy and Rényi entropy for generalized inverse exponential distribution is relatively high, overall Bayesian estimation performs better than maximum likelihood estimation. Finally, we demonstrate effectiveness of our estimation method in practical applications using a set of real data.

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Empirical E-Bayesian estimation of hierarchical poisson and gamma model using scaled squared error loss function

Cited by 3 publications

References 30 publications

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

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

Bayesian inference on parameters and reliability characteristics for inverse Xgamma distribution under adaptive-general progressive Type-II censoring

Statistical inference of entropy functions of generalized inverse exponential model under progressive type-II censoring test

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