Bayesian and non-Bayesian inference under adaptive type-II progressive censored sample with exponentiated power Lindley distribution

Hanan Haj Ahmad; Mukhtar M Salah; M S Eliwa; Ziyad Ali Alhussain; Ehab M Almetwally; Essam A Ahmed

doi:10.1080/02664763.2021.1931819

Bayesian and non-Bayesian inference under adaptive type-II progressive censored sample with exponentiated power Lindley distribution

J Appl Stat. 2021 May 31;49(12):2981-3001. doi: 10.1080/02664763.2021.1931819. eCollection 2022.

Authors

Hanan Haj Ahmad¹, Mukhtar M Salah², M S Eliwa³, Ziyad Ali Alhussain², Ehab M Almetwally⁴, Essam A Ahmed⁵

Affiliations

¹ Department of Basic Science, Preparatory Year Deanship, King Faisal University, Hofuf, Al-Ahsa, Saudi Arabia.
² Department of Mathematics, College of Science, Majmaah University, Al Majmaah, Saudi Arabia.
³ Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt.
⁴ Faculty of Business Administration, Delta University of Science and Technology, Egypt.
⁵ Faculty of Business Administration, Taibah University, Khyber, Saudi Arabia.

Abstract

This paper deals with the statistical inference of the unknown parameters of three-parameter exponentiated power Lindley distribution under adaptive progressive type-II censored samples. The maximum likelihood estimator (MLE) cannot be expressed explicitly, hence approximate MLEs are conducted using the Newton-Raphson method. Bayesian estimation is studied and the Markov Chain Monte Carlo method is used for computing the Bayes estimation. For Bayesian estimation, we consider two loss functions, namely: squared error and linear exponential (LINEX) loss functions, furthermore, we perform asymptotic confidence intervals and the credible intervals for the unknown parameters. A comparison between Bayes estimation and the MLE is observed using simulation analysis and we perform an optimally criterion for some suggested censoring schemes by minimizing bias and mean square error for the point estimation of the parameters. Finally, a real data example is used for the illustration of the goodness of fit for this model.

Keywords: Bayesian estimation; Exponentiated power Lindley; Markov chain Monte Carlo; adaptive progressive type-II censoring; maximum likelihood estimator; simulation.

Grants and funding

The authors extend their appreciation to the Deanship of Scientific Research at Majmaah University for funding this work under project number No. RGP-2019-2.