Bayesian parameter estimation of power function distribution under different loss functions

Ashraf Ali; Muhammad Zafar Iqbal; Madiha Ghamkhar; Adeel Anjum; Hafiz Bilal Murtaza

Author(s)

Ashraf Ali Department of Mathematics and Statistics University of Agriculture Faisalabad, Pakistan

Muhammad Zafar Iqbal Department of Mathematics and Statistics University of Agriculture Faisalabad,,Pakistan

Madiha Ghamkhar Department of Mathematics and Statistics University of Agriculture Faisalabad, Pakistan

Adeel Anjum Department of Mathematics and Statistics University of Agriculture Faisalabad, Pakistan

Hafiz Bilal Murtaza Department of Mathematics and Statistics University of Agriculture Faisalabad, Pakistan

Abstract

In statistical inference and real world, the Bayesian analysis is a modern parameter estimation technique. We have used power function distribution (PFD) and informative prior (Gamma Distribution) to find the Bayes estimators of parameter f under various loss functions: The square error loss function (SELF), the quadratic error loss function (QELF), the weighted square error loss function (WSELF), the precautionary error loss function (PELF), the K loss function (KLF), the entropy error loss function (EELF), the modified linear exponential error loss function (MLINEXELF) and the non-linear exponential error loss function (NLINEXLF). Furthermore, we compared the Bayes Estimators with the classical Maximum Likelihood Estimator (MLE) to evaluate their performance in terms of loss functions. Finally, the results have been shown graphically by using R software.

Publication Details

Page(s) 315-334

DOI DOI not available

Published Journal: Pakistan Journal of Statistics, Volume: 40, Issue: 3, Year: 2024

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Keywords

Gamma Distribution, Bayesian parameter, power function distribution

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