Point Estimation of Poisson Parameter by Bayesian Approach under Different Loss Functions.
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| Title: | Point Estimation of Poisson Parameter by Bayesian Approach under Different Loss Functions. |
|---|---|
| Authors: | Supharakonsakun, Yadpirun1 yadpirun.suph@pcru.ac.th, Phuwong, Nitaya2 nittayapornm16@gmail.com, Khamnang, Chitchanok2 chitchanok43702@gmail.com |
| Source: | IAENG International Journal of Applied Mathematics. Nov2024, Vol. 54 Issue 11, p2440-2458. 19p. |
| Subjects: | Monte Carlo method, Fix-point estimation, Parameter estimation, Poisson distribution, Error functions, Bayes' estimation |
| Abstract: | In the classical Poisson model, the distribution represents the number of events occurring within a given time or spatial interval. This study introduces new Bayesian methods for point estimation of the Poisson parameter, utilizing precautionary, entropy, and general entropy loss functions, particularly focusing on cases where the constants are c = 2 and 3. These methods are compared to traditional Bayesian estimators based on squared error and quadratic loss functions. A Monte Carlo simulation study was conducted to evaluate the performance of the proposed estimators, using mean squared error (MSE) as the primary criterion. The results demonstrate that the Bayesian approach, employing quadratic, entropy, and general entropy loss functions with c = 2, provided the most accurate estimates for smaller true parameter values ( λ = 0.5, 1, or 2), yielding the lowest MSE. For moderately larger true parameter values ( λ = 3, 5), the squared error and quadratic loss functions produced the minimum MSE across a range of sample sizes. For larger true parameter values ( λ = 10, 20, 30, and 50), the precautionary loss function exhibited superior performance. These findings underscore the versatility and accuracy of different Bayesian loss functions for Poisson parameter estimation under varying conditions. [ABSTRACT FROM AUTHOR] |
| Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: Point Estimation of Poisson Parameter by Bayesian Approach under Different Loss Functions. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Supharakonsakun%2C+Yadpirun%22">Supharakonsakun, Yadpirun</searchLink><relatesTo>1</relatesTo><i> yadpirun.suph@pcru.ac.th</i><br /><searchLink fieldCode="AR" term="%22Phuwong%2C+Nitaya%22">Phuwong, Nitaya</searchLink><relatesTo>2</relatesTo><i> nittayapornm16@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Khamnang%2C+Chitchanok%22">Khamnang, Chitchanok</searchLink><relatesTo>2</relatesTo><i> chitchanok43702@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Nov2024, Vol. 54 Issue 11, p2440-2458. 19p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Monte+Carlo+method%22">Monte Carlo method</searchLink><br /><searchLink fieldCode="DE" term="%22Fix-point+estimation%22">Fix-point estimation</searchLink><br /><searchLink fieldCode="DE" term="%22Parameter+estimation%22">Parameter estimation</searchLink><br /><searchLink fieldCode="DE" term="%22Poisson+distribution%22">Poisson distribution</searchLink><br /><searchLink fieldCode="DE" term="%22Error+functions%22">Error functions</searchLink><br /><searchLink fieldCode="DE" term="%22Bayes'+estimation%22">Bayes' estimation</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In the classical Poisson model, the distribution represents the number of events occurring within a given time or spatial interval. This study introduces new Bayesian methods for point estimation of the Poisson parameter, utilizing precautionary, entropy, and general entropy loss functions, particularly focusing on cases where the constants are c = 2 and 3. These methods are compared to traditional Bayesian estimators based on squared error and quadratic loss functions. A Monte Carlo simulation study was conducted to evaluate the performance of the proposed estimators, using mean squared error (MSE) as the primary criterion. The results demonstrate that the Bayesian approach, employing quadratic, entropy, and general entropy loss functions with c = 2, provided the most accurate estimates for smaller true parameter values ( λ = 0.5, 1, or 2), yielding the lowest MSE. For moderately larger true parameter values ( λ = 3, 5), the squared error and quadratic loss functions produced the minimum MSE across a range of sample sizes. For larger true parameter values ( λ = 10, 20, 30, and 50), the precautionary loss function exhibited superior performance. These findings underscore the versatility and accuracy of different Bayesian loss functions for Poisson parameter estimation under varying conditions. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 19 StartPage: 2440 Subjects: – SubjectFull: Monte Carlo method Type: general – SubjectFull: Fix-point estimation Type: general – SubjectFull: Parameter estimation Type: general – SubjectFull: Poisson distribution Type: general – SubjectFull: Error functions Type: general – SubjectFull: Bayes' estimation Type: general Titles: – TitleFull: Point Estimation of Poisson Parameter by Bayesian Approach under Different Loss Functions. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Supharakonsakun, Yadpirun – PersonEntity: Name: NameFull: Phuwong, Nitaya – PersonEntity: Name: NameFull: Khamnang, Chitchanok IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 19929978 Numbering: – Type: volume Value: 54 – Type: issue Value: 11 Titles: – TitleFull: IAENG International Journal of Applied Mathematics Type: main |
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