Estimation of Inverse Weibull Distribution Under Type-I Hybrid Censoring

TL;DR

This paper investigates statistical inference methods for the Inverse Weibull distribution under Type-I hybrid censoring, comparing maximum likelihood and Bayesian estimators through simulation and real data analysis.

Contribution

It introduces Bayesian estimation techniques for the Inverse Weibull distribution with hybrid censored data, including importance sampling and Lindley's approximation, which were not previously explored.

Findings

Bayesian estimators outperform MLE in small samples.

Importance sampling provides accurate Bayesian estimates.

Real data analysis validates the proposed methods.

Abstract

The hybrid censoring is a mixture of Type I and Type II censoring schemes. This paper presents the statistical inferences of the Inverse Weibull distribution when the data are Type-I hybrid censored. First we consider the maximum likelihood estimators of the unknown parameters. It is observed that the maximum likelihood estimators can not be obtained in closed form. We further obtain the Bayes estimators and the corresponding highest posterior density credible intervals of the unknown parameters under the assumption of independent gamma priors using the importance sampling procedure. We also compute the approximate Bayes estimators using Lindley's approximation technique. We have performed a simulation study and a real data analysis in order to compare the proposed Bayes estimators with the maximum likelihood estimators.