Shrinkage Testimators for the Shape Parameter of Pareto Distribution Using LINEX Loss Function

Bayesian estimators of Gini index and a Poverty measure are obtained in case of Pareto distribution under censored and complete setup. The said estimators are obtained using two noninformative priors, namely, uniform prior and Jeffreys’ prior, and one conjugate prior under the assumption of Linear Exponential (LINEX) loss function. Using simulation techniques, the relative efficiency of proposed estimators using different priors and loss functions is obtained. The performances of the proposed estimators have been compared on the basis of their simulated risks obtained under LINEX loss function.

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

Computational Intelligence and Neuroscience ◽

10.1155/2021/2101972 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Afrah Al-Bossly

Keyword(s):

Bayesian Estimation ◽

Loss Function ◽

Shape Parameter ◽

Likelihood Estimation ◽

Loss Functions ◽

Bayesian Estimator ◽

Linex Loss Function ◽

Lomax Distribution ◽

Linex Loss ◽

Asymmetric Loss Function

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.

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E-Bayesian analysis of the Gumbel type-ii distribution under type-ii censored scheme

International Journal of Advanced Mathematical Sciences ◽

10.14419/ijams.v3i2.5093 ◽

2015 ◽

Vol 3 (2) ◽

pp. 108 ◽

Cited By ~ 1

Author(s):

Hesham Reyad ◽

Soha Othman Ahmed

Keyword(s):

Loss Function ◽

Shape Parameter ◽

Quadratic Loss ◽

Type Ii ◽

Linex Loss Function ◽

Censored Samples ◽

Squared Error ◽

Linex Loss ◽

Symmetric Loss ◽

Bayesian Estimators

<p>This paper seeks to focus on Bayesian and E-Bayesian estimation for the unknown shape parameter of the Gumbel type-II distribution based on type-II censored samples. These estimators are obtained under symmetric loss function [squared error loss (SELF))] and various asymmetric loss functions [LINEX loss function (LLF), Degroot loss function (DLF), Quadratic loss function (QLF) and minimum expected loss function (MELF)]. Comparisons between the E-Bayesian estimators with the associated Bayesian estimators are investigated through a simulation study.</p>

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