Parameter Estimation of Inverted Exponentiated Half-Logistic Distribution under Progressive Type-II Censored Data with Competing Risks

Abstract

In this work, the statistical inference of inverted exponentiated half-logistic distribution is considered under the progressive type-II censored data with competing risks. The parameter estimations of the constant scale parameters but different shape parameters that changed due to various risk factors are investigated in this study. The maximum likelihood estimation is deduced to obtain the parameter estimators and asymptotic confidence intervals; meanwhile, the existence and uniqueness of the maximum likelihood estimators are discussed. Subsequently, bootstrap confidence intervals are calculated and presented. The Bayes estimates based on the square error loss function are derived using the Markov Chain Monte Carlo method. Then, the highest posterior density credible intervals are calculated and provided. Simulations are implemented to compare two kinds of estimates. For illustrative purposes, two experimental lifetime datasets from different fields are exhibited and analyzed. Finally, an optimal censoring scheme is suggested under two optimality criteria.