Maximum Likelihood Estimation and Bayesian Estimation of three-parameter Weibull Distribution Based on Interval-Censored Data

Abstract

The interval-censored data is that represents adjacent inspection times that surround an unknown failure time. This paper gives a review of the classical approach of the maximum likelihood estimating method to parameters of three-parameters Weibull distribution with interval-censored data. It also considers the Bayes’ estimators under asymmetric three loss functions squared error loss (SEL), linear-exponential (LINEX), and generalized entropy loss (GEL) functions. For the unknown parameters of three-parameters Weibull distributions with interval-censored data. We use Lindley’s approximation to compute the Bayes estimates. Then we will apply a Monte Carlo simulation study is carried out to compare the performances of the methods using the R programming language to compute and compare the performance of the proposed estimators. A real data application is also presented. The study observed that the Bayesian estimator under generalized entropy loss (GEL) functions is preferred over the classical maximum likelihood estimator for all parameters of scale, shape, and location.