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E-Bayesian Estimation of the Negative Binomial Distribution Reliability

Zhongbo Hu

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Abstract

In this paper,under entropy loss function,the Bayesian estimation,the E-Bayesian estimation and hierarchical Bayesian estimation of the negative binomial distribution reliability θ with the Beta distribution and the power distribution as its prior distribution are given.The numerical results show that the E-Bayesian estimation of θ with the power distribution as its prior distribution is more robust and easier to calculate than its hierarchical Bayesian estimation.

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What this paper is about

In this paper,under entropy loss function,the Bayesian estimation,the E-Bayesian estimation and hierarchical Bayesian estimation of the negative binomial distribution reliability θ with the Beta distribution and the power distribution as its prior distribution are given.The numerical results show that the E-Bayesian estimation of θ with the power distribution as its prior distribution is more robust and easier to calculate than its hierarchical Bayesian estimation.

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Available abstract

In this paper,under entropy loss function,the Bayesian estimation,the E-Bayesian estimation and hierarchical Bayesian estimation of the negative binomial distribution reliability θ with the Beta distribution and the power distribution as its prior distribution are given.The numerical results show that the E-Bayesian estimation of θ with the power distribution as its prior distribution is more robust and easier to calculate than its hierarchical Bayesian estimation.

Key concepts: Bayes estimator, Bayesian linear regression, Beta-binomial distribution, Bayesian hierarchical modeling, Bayesian probability, Mathematics, Negative binomial distribution, Statistics

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