Bayesian survival analysis for adaptive Type-II progressive hybrid censored Hjorth data

• Published in: Computational statistics Vol. 36; no. 3; pp. 1965 - 1990
• Main Authors: Elshahhat, Ahmed, Nassar, Mazen
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2021; Springer Nature B.V
• Subjects: Bayesian analysis; Confidence intervals; Economic Theory/Quantitative Economics/Mathematical Methods; Electronic devices; Estimators; Markov chains; Mathematics and Statistics; Monte Carlo simulation; Original Paper; Parameter estimation; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Statistical analysis; Statistics; Survival; Survival analysis; Maximum likelihood estimator; Metropolis-Hasting algorithm; 62N01; 62N02; Hjorth distribution; Bayes estimator; Reliability characteristics; 62N05; 62F10; Lindley’s approximation method; Adaptive Type-II progressive hybrid censoring scheme; 62F15
• DOI: 10.1007/s00180-021-01065-8
• ISSN: 0943-4062

Adaptive Type-II progressive hybrid censoring scheme has been proposed to increase the efficiency of statistical analysis and save the total test time on a life-testing experiment. This article deals with the problem of estimating the parameters, survival and hazard rate functions of the two-parameter Hjorth distribution under adaptive Type-II progressive hybrid censoring scheme using maximum likelihood and Bayesian approaches. The two-sided approximate confidence intervals of the unknown quantities are constructed. Under the assumption of independent gamma priors, the Bayes estimators are obtained using squared error loss function. Since the Bayes estimators cannot be expressed in closed forms, Lindley’s approximation and Markov chain Monte Carlo methods are considered and the highest posterior density credible intervals are also obtained. To study the behavior of the various estimators, a Monte Carlo simulation study is performed. The performances of the different estimators have been compared on the basis of their average root mean squared error and relative absolute bias. Finally, to show the applicability of the proposed estimators a data set of industrial devices has been analyzed.