Bayesian Estimations from the Two-Parameter Bathtub-Shaped Lifetime Distribution Based on Record Values

Mahmoud Ali Selim

Abstract


This article discusses Bayesian and non-Bayesian estimations problems of the unknown parameters for the two-parameter bathtub-shaped lifetime distribution based on upper record values. The ML and the Bayes estimates based on record values are derived for the two unknown parameters as well as hazard function. When the Bayesian approach is considered, under the assumption that both parameters are unknown, the Bayes estimators cannot be obtained in explicit forms. An approximation form due to Soland (Soland (1969)) is used for obtaining the Bayes estimates based on a conjugate prior for the first shape parameter and a discrete prior for the second shape parameter of this model. This is done with respect to the squared error loss and LINEX loss functions. The estimation procedure is then applied to real data set and simulation data.


Keywords


Bayesian; Upper record values; Maximum likelihood; Soland's method

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DOI: http://dx.doi.org/10.18187/pjsor.v8i2.328

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Title

Bayesian Estimations from the Two-Parameter Bathtub-Shaped Lifetime Distribution Based on Record Values

Keywords

Bayesian; Upper record values; Maximum likelihood; Soland's method

Description

This article discusses Bayesian and non-Bayesian estimations problems of the unknown parameters for the two-parameter bathtub-shaped lifetime distribution based on upper record values. The ML and the Bayes estimates based on record values are derived for the two unknown parameters as well as hazard function. When the Bayesian approach is considered, under the assumption that both parameters are unknown, the Bayes estimators cannot be obtained in explicit forms. An approximation form due to Soland (Soland (1969)) is used for obtaining the Bayes estimates based on a conjugate prior for the first shape parameter and a discrete prior for the second shape parameter of this model. This is done with respect to the squared error loss and LINEX loss functions. The estimation procedure is then applied to real data set and simulation data.


Date

2012-03-28

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol 8. No. 2, 2012



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