BAYESIAN ESTIMATION OF THE SHAPE PARAMETER OF THE GENERALISED EXPONENTIAL DISTRIBUTION UNDER DIFFERENT LOSS FUNCTIONS

SANKU DEY

Abstract


The generalized exponential (GE) distribution proposed by Gupta and Kundu (1999) is an important lifetime distribution in survival analysis. In this article, we propose to obtain Bayes estimators and its associated risk based on a class of  non-informative prior under the assumption of three loss functions, namely, quadratic loss function (QLF), squared log-error loss function (SLELF) and general entropy loss function (GELF). The motivation is to explore the most appropriate loss function among these three loss functions. The performances of the estimators are, therefore, compared on the basis of their risks obtained under QLF, SLELF and GELF separately. The relative efficiency of the estimators is also obtained. Finally, Monte Carlo simulations are performed to compare the performances of the Bayes estimates under different situations.


Keywords


Bayes estimator, prior distribution, loss functions, root mean square error(rmse), efficiency.

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DOI: http://dx.doi.org/10.18187/pjsor.v6i2.147

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Title

BAYESIAN ESTIMATION OF THE SHAPE PARAMETER OF THE GENERALISED EXPONENTIAL DISTRIBUTION UNDER DIFFERENT LOSS FUNCTIONS

Keywords

Bayes estimator, prior distribution, loss functions, root mean square error(rmse), efficiency.

Description

The generalized exponential (GE) distribution proposed by Gupta and Kundu (1999) is an important lifetime distribution in survival analysis. In this article, we propose to obtain Bayes estimators and its associated risk based on a class of  non-informative prior under the assumption of three loss functions, namely, quadratic loss function (QLF), squared log-error loss function (SLELF) and general entropy loss function (GELF). The motivation is to explore the most appropriate loss function among these three loss functions. The performances of the estimators are, therefore, compared on the basis of their risks obtained under QLF, SLELF and GELF separately. The relative efficiency of the estimators is also obtained. Finally, Monte Carlo simulations are performed to compare the performances of the Bayes estimates under different situations.


Date

2010-11-15

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol 6. No. 2, July 2010



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810