Brazilian Journal of Probability and Statistics

Bayesian inference on power Lindley distribution based on different loss functions

Abbas Pak, M. E. Ghitany, and Mohammad Reza Mahmoudi

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Abstract

This paper focuses on Bayesian estimation of the parameters and reliability function of the power Lindley distribution by using various symmetric and asymmetric loss functions. Assuming suitable priors on the parameters, Bayes estimates are derived by using squared error, linear exponential (linex) and general entropy loss functions. Since, under these loss functions, Bayes estimates of the parameters do not have closed forms we use lindley’s approximation technique to calculate the Bayes estimates. Moreover, we obtain the Bayes estimates of the parameters using a Markov Chain Monte Carlo (MCMC) method. Simulation studies are conducted in order to evaluate the performances of the proposed estimators under the considered loss functions. Finally, analysis of a real data set is presented for illustrative purposes.

Article information

Source
Braz. J. Probab. Stat., Volume 33, Number 4 (2019), 894-914.

Dates
Received: June 2017
Accepted: December 2018
First available in Project Euclid: 26 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1566806437

Digital Object Identifier
doi:10.1214/18-BJPS428

Mathematical Reviews number (MathSciNet)
MR3996321

Keywords
Power Lindley distribution Bayesian estimation maximum likelihood estimation squared error loss function asymmetric loss function

Citation

Pak, Abbas; Ghitany, M. E.; Mahmoudi, Mohammad Reza. Bayesian inference on power Lindley distribution based on different loss functions. Braz. J. Probab. Stat. 33 (2019), no. 4, 894--914. doi:10.1214/18-BJPS428. https://projecteuclid.org/euclid.bjps/1566806437


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