Empirical E-Bayesian estimation for the parameter of Poisson distribution

Heba S. Mohammed; Heba S. Mohammed

doi:10.3934/math.2021475

AIMS Mathematics

2021, Volume 6, Issue 8: 8205-8220. doi: 10.3934/math.2021475

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Research article

Empirical E-Bayesian estimation for the parameter of Poisson distribution

Heba S. Mohammed ^{1,2
,
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1.
Mathematical Sciences Department, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, New Valley University, El-Kharga, 72511, Egypt

Received: 19 February 2021 Accepted: 19 May 2021 Published: 26 May 2021
MSC : 62F10, 62F15

This paper introduces a new method of estimation, empirical E-Bayesian estimation. In this method, we consider the hyperparameters of E-Bayesian estimation are unknown. We compute the E-Bayesian and empirical E-Bayesian estimates for the parameter of Poisson distribution based on a complete sample. For our purpose, we consider the case of the squared error loss function. The E-posterior risk and empirical E-posterior risk are computed. A comparison between E-Bayesian and empirical E- Bayesian methods with the corresponding maximum likelihood estimation is made using the Monte Carlo simulation. A relevant application is utilized to illustrate the applicability of multiple estimators.
- Poisson distribution,
- E-Bayesian estimation,
- empirical E-Bayesian estimation,
- E-posterior risk,
- empirical E-posterior risk
Citation: Heba S. Mohammed. Empirical E-Bayesian estimation for the parameter of Poisson distribution[J]. AIMS Mathematics, 2021, 6(8): 8205-8220. doi: 10.3934/math.2021475

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Abstract

This paper introduces a new method of estimation, empirical E-Bayesian estimation. In this method, we consider the hyperparameters of E-Bayesian estimation are unknown. We compute the E-Bayesian and empirical E-Bayesian estimates for the parameter of Poisson distribution based on a complete sample. For our purpose, we consider the case of the squared error loss function. The E-posterior risk and empirical E-posterior risk are computed. A comparison between E-Bayesian and empirical E- Bayesian methods with the corresponding maximum likelihood estimation is made using the Monte Carlo simulation. A relevant application is utilized to illustrate the applicability of multiple estimators.

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