Estimation of the Coefficient of Variation of Weibull Distribution under Type-I Progressively Interval Censoring: A Simulation-based Approach

TL;DR

This paper develops and compares new methods for estimating the coefficient of variation of Weibull distributions under type-I censored data, using simulation and real data applications.

Contribution

It introduces a nonlinear least squares approach and Bayesian methods for estimating Weibull CV under censored data, with comprehensive simulation and real data validation.

Findings

Least squares and Bayesian methods yield better point estimates.

Highest posterior density intervals often outperform other interval estimates.

Methods are validated through simulation and real data application.

Abstract

Measures of relative variability, such as the Pearson's coefficient of variation (CV$_p$), give much insight into the spread of lifetime distributions, like the Weibull distribution. The estimation of the Weibull CV$_p$ in modern statistics has traditionally been prioritized only when complete data is available. In this article, we estimate the Weibull CV$_p$ and its second-order alternative, denoted as CV$_k$, under type-I progressively interval censoring, which is a typical scenario in survival analysis and reliability theory. Point estimates are obtained using the methods of maximum likelihood, least squares, and the Bayesian approach with MCMC simulation. A nonlinear least squares method is proposed for estimating the CV$_p$ and CV$_k$. We also perform interval estimation of the CV$_p$ and CV$_k$ using the asymptotic confidence intervals, bootstrap intervals through the least squares estimates, and the highest posterior density intervals. A comprehensive Monte Carlo simulation study is carried out to understand and compare the performance of the estimators. The proposed least squares and the Bayesian methods produce better point estimates for the CV$_p$. The highest posterior density intervals outperform other interval estimates in many cases. The methodologies are also applied to a real dataset to demonstrate the performance of the estimators.