E-Bayesian Estimation for the Weibull Distribution under Adaptive Type-I Progressive Hybrid Censored Competing Risks Data

Hassan Okasha; Abdelfattah Mustafa

doi:10.3390/e22080903

E-Bayesian Estimation for the Weibull Distribution under Adaptive Type-I Progressive Hybrid Censored Competing Risks Data

Entropy (Basel). 2020 Aug 17;22(8):903. doi: 10.3390/e22080903.

Authors

Hassan Okasha^{1

2}, Abdelfattah Mustafa^{3

4}

Affiliations

¹ Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
² Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo 11884, Egypt.
³ Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia.
⁴ Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.

Abstract

This article focuses on using E-Bayesian estimation for the Weibull distribution based on adaptive type-I progressive hybrid censored competing risks (AT-I PHCS). The case of Weibull distribution for the underlying lifetimes is considered assuming a cumulative exposure model. The E-Bayesian estimation is discussed by considering three different prior distributions for the hyper-parameters. The E-Bayesian estimators as well as the corresponding E-mean square errors are obtained by using squared and LINEX loss functions. Some properties of the E-Bayesian estimators are also derived. A simulation study to compare the various estimators and real data application is applied to show the applicability of the different estimators are proposed.

Keywords: Bayesian estimation; E-Bayesian estimation; E-mean-square error; adaptive type-I progressive hybrid censored; competing risks; cumulative exposure model.