Inferences and Optimal Censoring Schemes for Progressively First-Failure Censored Nadarajah-Haghighi Distribution

A new extension of the exponential distribution, proposed by Nadarajah and Haghighi (Statistics 45, 543–558 (2011)), is an alternative to the gamma, Weibull and generalized-exponential models, it is also known as NH distribution. The maximum likelihood and Bayes inferential approaches for estimating the unknown two-parameters and some lifetime parameters such as survival and hazard rate functions of the NH distribution in presence of progressive first-failure censored sampling are considered. Based on observed Fisher’s information matrix, the approximate confidence intervals for the two-parameters, and any function of them, are constructed. Using Lindley’s approximation and Markov chain Monte Carlo methods under the assumption of conjugate gamma priors, the Bayes estimates and associate highest posterior density credible intervals for the unknown parameters and reliability characteristics are developed based on squared error loss function. Although the proposed estimators cannot be expressed in explicit forms, these can be easily obtained through the use of appropriate numerical techniques. A Monte Carlo simulation study is carried out to examine the performance of proposed methods. Using different optimality criteria, an optimal censoring scheme has been suggested. Finally, a real data set is analyzed for illustration purposes.