Estimation of Reliability Indices for Alpha Power Exponential Distribution Based on Progressively Censored Competing Risks Data

Mazen Nassar, Refah Alotaibi and Chunfang Zhang
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Mazen Nassar: Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Refah Alotaibi: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Chunfang Zhang: School of Mathematics and Statistics, Xidian University, Xi’an 710126, China

Mathematics, 2022, vol. 10, issue 13, 1-25

Abstract: In reliability analysis and life testing studies, the experimenter is frequently interested in studying a specific risk factor in the presence of other factors. In this paper, the estimation of the unknown parameters, reliability and hazard functions of alpha power exponential distribution is considered based on progressively Type-II censored competing risks data. We assume that the latent cause of failures has independent alpha power exponential distributions with different scale and shape parameters. The maximum likelihood method is considered to estimate the model parameters as well as the reliability and hazard rate functions. The approximate and two parametric bootstrap confidence intervals of the different estimators are constructed. Moreover, the Bayesian estimation method of the unknown parameters, reliability and hazard rate functions are obtained based on the squared error loss function using independent gamma priors. To get the Bayesian estimates as well as the highest posterior credible intervals, the Markov Chain Monte Carlo procedure is implemented. A comprehensive simulation experiment is conducted to compare the performance of the proposed procedures. Finally, a real dataset for the relapse of multiple myeloma with transplant-related mortality is analyzed.

Keywords: alpha power exponential distribution; progressive Type-II censoring; competing risks; maximum likelihood; bayesian estimation; loss function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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