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.

翻译：相对变异性的度量，如皮尔逊变异系数（CV$_p$），对威布尔分布等寿命分布的离散程度提供了重要洞察。在现代统计学中，威布尔分布CV$_p$的估计传统上仅在完整数据可用时被优先考虑。本文在生存分析和可靠性理论中的典型场景——I型逐步区间删失条件下，估计威布尔分布的CV$_p$及其二阶替代指标（记为CV$_k$）。点估计通过极大似然法、最小二乘法以及基于MCMC模拟的贝叶斯方法获得。针对CV$_p$和CV$_k$的估计，提出了一种非线性最小二乘法。同时采用渐近置信区间、基于最小二乘估计的自举区间以及最高后验密度区间对CV$_p$和CV$_k$进行区间估计。通过全面的蒙特卡洛仿真研究来理解和比较各估计量的性能。所提出的最小二乘法和贝叶斯方法对CV$_p$能产生更优的点估计结果。在多数情况下，最高后验密度区间优于其他区间估计方法。本文方法还通过实际数据集验证了估计量的性能。