E-Bayesian and Bayesian Estimation for the Lomax Distribution under Weighted Composite LINEX Loss Function.

Afrah Al-Bossly,Ahmed Mostafa Khalil

doi:10.1155/2021/2101972

Afrah Al-Bossly, Ahmed Mostafa Khalil

Open Access

https://doi.org/10.1155/2021/2101972

Copy DOI

Abstract

The main contribution of this work is the development of a compound LINEX loss function (CLLF) to estimate the shape parameter of the Lomax distribution (LD). The weights are merged into the CLLF to generate a new loss function called the weighted compound LINEX loss function (WCLLF). Then, the WCLLF is used to estimate the LD shape parameter through Bayesian and expected Bayesian (E-Bayesian) estimation. Subsequently, we discuss six different types of loss functions, including square error loss function (SELF), LINEX loss function (LLF), asymmetric loss function (ASLF), entropy loss function (ENLF), CLLF, and WCLLF. In addition, in order to check the performance of the proposed loss function, the Bayesian estimator of WCLLF and the E-Bayesian estimator of WCLLF are used, by performing Monte Carlo simulations. The Bayesian and expected Bayesian by using the proposed loss function is compared with other methods, including maximum likelihood estimation (MLE) and Bayesian and E-Bayesian estimators under different loss functions. The simulation results show that the Bayes estimator according to WCLLF and the E-Bayesian estimator according to WCLLF proposed in this work have the best performance in estimating the shape parameters based on the least mean averaged squared error.

Highlights

Introduction e expectedBayesian estimator is a new criterion for estimating the parameters, reliability and hazard functions, which consist of obtaining the expectation of Bayesian estimates with respect to the distributions of hyperparameters [1]
Ese estimators are derived under squared error, entropy, and prophylactic loss functions [10]. e main purpose of this study is to develop a compound LINEX loss function (CLLF) and use Bayesian and E-Bayesian estimators to estimate the shape parameters of the Lomax distribution (LD). en, it will compare the proposed estimator with other methods including, maximum likelihood estimation (MLE), and Bayesian and E-Bayesian estimators under square error loss function (SELF), AS LF, entropy loss function (ENLF), and CLLF
CLLF is developed to estimate the shape parameter of LD. e development occurred through merging the weights into the CLLF to generate a new loss function called the weighted compound LINEX loss function (WCLLF)

Summary

Introduction

Introduction e expectedBayesian estimator is a new criterion for estimating the parameters, reliability and hazard functions, which consist of obtaining the expectation of Bayesian estimates with respect to the distributions of hyperparameters [1]. E researcher proposes this loss function depending on weighting CLLF as follows: Lw(β􏽢, β) w (β)L(β􏽢, β) w(β)Lc(β􏽢, β) + w(β)L− c(β􏽢, β) w(β)exp[− c(β􏽢, β)] + w(β)exp[c(β􏽢, β)] − 2, c > 0, (19) We use six different loss functions, including SELF, ASLF, ENLF, LLF, CLLF, and WCLLF.

Results

Conclusion