Bayesian inference of Unit Gompertz distribution based on dual generalized order statistics

Abstract

In this article, we consider the estimation problem of Unit Gompertz distribution with parameters α and β under the framework of dual generalized order statistics. This article is purely devoted to present the Bayesian view of estimation of Unit Gompertz distribution. For this purpose, we consider two widely popular approximation methods called Markov chain Monte Carlo and Lindley approximation methods. The results are derived under the symmetric (squared error) and asymmetric (Linear exponential and General entropy) loss functions. Since the order statistics and lower record values are the particular cases of the dual generalized order statistics, a simulation study is provided for order statistics and lower record values to observe the behavior of estimators. The average lengths of highest posterior density intervals of α, β, and R(t) are calculated for 95% confidence coefficient. Finally, real data applications are reported for lower record values and order statistics, separately, to show the practical aspects of the derived results.

Keywords:

• Dual generalized order statistics
• Lindley approximation
• Markov chain Monte Carlo
• Unit-Gompertz distribution

Acknowledgments

The authors are thankful to the editor and anonymous referees for their constructive and helpful comments which have significantly improved the article.

Disclosure statement

No potential competing interest was reported by the author(s).

Additional information

Funding

The first author would like to thank Science and Engineering Research Board, DST, Government of India [MATRICS Grant: MTR/2018/000084] for providing financial support.