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

TL;DR

This study addresses estimating the Weibull distribution's relative variability via $CV_p$ and $CV_k$ under type-I progressively interval censoring. It develops and compares three estimation paradigms—maximum likelihood, linear/nonlinear least squares, and Bayesian MCMC—with emphasis on point accuracy and interval reliability, including bootstrap and HPD methods. A thorough Monte Carlo evaluation shows that Bayesian methods with informative priors and the proposed least squares estimators give superior point estimates for the CVs, while HPD intervals often yield the best coverage; longer monitoring schemes tend to improve estimator performance. The authors validate the approaches on a real survival dataset, demonstrating practical applicability to reliability and survival analyses where censoring is prevalent. Overall, the work advances robust estimation of Weibull CV under censoring and provides actionable guidance for interval estimation in applied settings, with potential extensions to survival and hazard-rate inference.

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.

Figures (5)

• Figure 1: Progressively Type-I Interval Censored Lifetime Data of Plasma Cell Myeloma Patients
• Figure 2: The interval estimates of the various parameters using real data
• Figure 3: (a-b) Least Squares surface plots of the objective functions (c-d) curve fitting using real data
• Figure 4: Traceplots for the generated MCMC samples from each parameter's posterior distribution
• Figure 5: Histograms representing the posterior distribution of the generated MCMC samples with the corresponding HPDIs