Inference of progressively type-II censored competing risks data from Chen distribution with an application

Abstract

In this paper, the estimation of unknown parameters of Chen distribution is considered under progressive Type-II censoring in the presence of competing failure causes. It is assumed that the latent causes of failures have independent Chen distributions with the common shape parameter, but different scale parameters. From a frequentist perspective, the maximum likelihood estimate of parameters via expectation–maximization (EM) algorithm is obtained. Also, the expected Fisher information matrix based on the missing information principle is computed. By using the obtained expected Fisher information matrix of the MLEs, asymptotic 95% confidence intervals for the parameters are constructed. We also apply the bootstrap methods (Bootstrap-p and Bootstrap-t) to construct confidence intervals. From Bayesian aspect, the Bayes estimates of the unknown parameters are computed by applying the Markov chain Monte Carlo (MCMC) procedure, the average length and coverage rate of credible intervals are also carried out. The Bayes inference is based on the squared error, LINEX, and general entropy loss functions. The performance of point estimators and confidence intervals is evaluated by a simulation study. Finally, a real-life example is considered for illustrative purposes.

Keywords:

• Competing risks
• progressively type-II censoring
• EM algorithm
• bootstrap
• Bayesian estimation
• Markov chain Monte Carlo

2010 Mathematics Subject Classifications:

• 62F10
• 62F15
• 62F40

Acknowledgments

The authors would like to thank the Editor and reviewers for their valuable comments and suggestions to improve the presentation of the paper. The authors extend their appreciation to the Deanship of Scientific at Majmaah University for funding this work through research project No. (RGP-2019-2).

Disclosure statement

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

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

The authors extend their appreciation to the Deanship of Scientific at Majmaah University for funding this work through research project No. (RGP-2019-2).