Empirical E-Bayesian estimation for the parameter of Poisson distribution
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....
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-05-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2021475?viewType=HTML |
| _version_ | 1819067522913140736 |
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| author | Heba S. Mohammed |
| author_facet | Heba S. Mohammed |
| author_sort | Heba S. Mohammed |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-21T16:19:36Z |
| format | Article |
| id | doaj.art-fb97358ced744538884953a6dc504560 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-21T16:19:36Z |
| publishDate | 2021-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-fb97358ced744538884953a6dc5045602022-12-21T18:57:37ZengAIMS PressAIMS Mathematics2473-69882021-05-01688205822010.3934/math.2021475Empirical E-Bayesian estimation for the parameter of Poisson distributionHeba S. Mohammed01. 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, EgyptThis 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.https://www.aimspress.com/article/doi/10.3934/math.2021475?viewType=HTMLpoisson distributione-bayesian estimationempirical e-bayesian estimatione-posterior riskempirical e-posterior risk |
| spellingShingle | Heba S. Mohammed Empirical E-Bayesian estimation for the parameter of Poisson distribution AIMS Mathematics poisson distribution e-bayesian estimation empirical e-bayesian estimation e-posterior risk empirical e-posterior risk |
| title | Empirical E-Bayesian estimation for the parameter of Poisson distribution |
| title_full | Empirical E-Bayesian estimation for the parameter of Poisson distribution |
| title_fullStr | Empirical E-Bayesian estimation for the parameter of Poisson distribution |
| title_full_unstemmed | Empirical E-Bayesian estimation for the parameter of Poisson distribution |
| title_short | Empirical E-Bayesian estimation for the parameter of Poisson distribution |
| title_sort | empirical e bayesian estimation for the parameter of poisson distribution |
| topic | poisson distribution e-bayesian estimation empirical e-bayesian estimation e-posterior risk empirical e-posterior risk |
| url | https://www.aimspress.com/article/doi/10.3934/math.2021475?viewType=HTML |
| work_keys_str_mv | AT hebasmohammed empiricalebayesianestimationfortheparameterofpoissondistribution |