Point Estimation of Poisson Parameter by Bayesian Approach under Different Loss Functions.

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Bibliographic Details
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]
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Database:	Engineering Source

Description
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]
ISSN:	19929978