Statistical inference of dependent competing risks from Marshall–Olkin bivariate Burr-XII distribution under complex censoring

Abstract

Dealing with competing risks is an important problem in reliability analysis and attracts much attention from scholars. It is more practical to consider competing risks with dependent failure causes in reality. In this article, statistical inference of the Marshall–Olkin bivariate Burr-XII distribution under adaptive type-II progressive hybrid censoring is discussed to show the procedure of dependent competing risks analysis in the complex data structure. The maximum likelihood estimation and lognormal approximation confidence intervals of parameters are computed. The existence and uniqueness of solutions are proved with Cauchy-Schwarz inequality. The Bayesian method with Gamma-Dirichlet prior and Metropolis-Hastings algorithm are further considered to find satisfied estimation of parameters. In addition, dynamic cumulative residual entropy is derived to quantify the information uncertainty of data. We finally compare the performance of various methods by conducting a simulation study and real data analysis.

Keywords:

• Adaptive type-II progressive hybrid censoring
• Bivariate Burr-XII distribution
• Bayesian analysis
• Dependent competing risks
• Gamma-Dirichlet prior
• Maximum likelihood estimation
• Metropolis-Hastings algorithm

Acknowledgments

Wenhao’s work was partially supported by the Fund of China Academy of Railway Sciences Corporation Limited (No. 2020YJ120). The authors would like to thank the editor and anonymous referees for their constructive comments and suggestions that have substantially improved the original manuscript.