Bayesian analysis of an exponentiated half-logistic distribution under progressively type-II censoring

Abstract

Abstract This paper develops maximum likelihood estimators (MLEs) of unknown param-eters in an exponentiated half-logistic distribution based on a progressively type-IIcensored sample. We obtain approximate con dence intervals for the MLEs by usingasymptotic variance and covariance matrices. Using importance sampling, we obtainBayes estimators and corresponding credible intervals with the highest posterior densityand Bayes predictive intervals for unknown parameters based on progressively type-IIcensored data from an exponentiated half logistic distribution. For illustration pur-poses, we examine the validity of the proposed estimation method by using real andsimulated data.Keywords: Bayes predictive interval, exponentiated half-logistic distribution, HPD cred-ible interval, importance sampling, progressively type-II censored sample. 1. Introduction Many reliability and survival analysis studies have used half-logistic distributions, partic-ularly for censored data. Several studies have drawn inferences about half logistic distribu-tions. Balakrishnan and Puthenpura (1986) introduce the best linear unbiased estimator oflocation and scale parameters of half-logistic distributions by considering linear functionsof order statistics. Balakrishnan and Wong (1991) obtain approximate maximum likelihoodestimators (AMLEs) of location and scale parameters of half-logistic distributions by usinga type-II right-censored sample. Kang et al. (2008) derive AMLEs and MLEs of scale pa-rameters of half-logistic distributions by using progressively type-II censored samples. Kanget al. (2009) propose AMLEs of scale parameters of half-logistic distributions by consideringdouble-hybrid censored samples. Kang and Seo (2011) recently examine exponentiated half-logistic distributions and propose two types of AMLEs of scale parameters and reliabilityfunctions by using progressively type-II right-censored samples. Kim et al. (2011a) deriveBayesian estimators of shape parameters, reliability functions, and failure rate functions