Bayesian estimation of the reliability characteristic of Shanker distribution

• Main Author: Tahani A. Abushal
• Format: Article
• Language: English
• Published: SpringerOpen 2019-08-01
• Series: Journal of the Egyptian Mathematical Society
• Subjects: Shanker distribution; Maximum likelihood estimate; Bootstrap technique; Metropolis-hastings algorithm
• Online Access: http://link.springer.com/article/10.1186/s42787-019-0033-x

Abstract In this study, we discussed the Bayesian property of unknown parameter and reliability characteristic of the Shanker distribution. The maximum likelihood estimate is calculated. The approximate confidence interval of the unknown parameter is constructed based on the asymptotic normality of maximum likelihood estimator. Two bootstrap confidence intervals for the unknown parameter are also computed. Bayesian estimates of parameter and reliability characteristic against squared error loss function are obtained. Lindley’s approximation and Metropolis-Hastings algorithm are applied to obtain the Bayes estimates. In consequence, we also construct the highest posterior density intervals. A numerical comparison is also made to compare different methods through a Monte Carlo simulation study. Finally, two real data sets are also analyzed using the proposed methods.