Classical and Bayesian estimation of the reliability characteristics for logistic-exponential distribution

Abstract

The basic tool for studying the ageing and associated characteristics of any lifetime equipments is the reliability/survival function. It is common practice that while estimating the parameters of a model, one usually adopt maximum likelihood estimation method as the starting point as a classical method of estimation. In this paper, we consider maximum product of spacing estimation, besides using maximum likelihood method for estimating the reliability characteristics, such as, mean time to system failure (MTSF), reliability function (RF) and hazard rate function (HF) at a specified time point \(t_0\) for logistic-exponential distribution. In addition, three bootstrap methods are considered for obtaining confidence intervals of MTSF, RT and HF. Besides, Bayesian estimation method is considered under symmetric as well as asymmetric loss functions using gamma priors for both shape and scale parameters for the considered model. Further, highest posterior density credible intervals are obtained by using a Markov chain Monte Carlo method with Gibbs sampler under Metropolis–Hastings sampling procedure. Average widths and coverage probabilities for each confidence intervals are computed. A Monte Carlo simulation study is carried out to compare the performance of the proposed estimates. Finally, two real data sets have been re-analyzed for illustrative purposes.