🤖 AI Summary
This study addresses the challenge of accurately estimating relative variability—such as the coefficient of variation—for the power Lindley distribution under progressive Type-I interval censoring. It presents the first systematic investigation of estimation methods in this setting, integrating both frequentist and Bayesian paradigms. The proposed frequentist approaches include point estimators based on midpoint approximation, maximum likelihood, method of moments, nonlinear least squares, and Bootstrap resampling, along with asymptotic and Bootstrap confidence intervals. Bayesian inference is implemented via slice sampling for posterior analysis. Extensive simulations and a real-data application demonstrate that the proposed methods are effective and feasible, with the Bayesian approach consistently yielding superior estimation accuracy and stability across various censoring schemes and sample sizes, while also offering guidance for optimal inspection interval design.
📝 Abstract
The measures of relative variability, such as the coefficient of variation, are estimated for the Power Lindley distribution using progressive type-I interval-censored data. Both Bayesian and frequentist approaches are applied, including the midpoint approximation, maximum likelihood estimation, method of moments, bootstrap, and non-linear least squares methods. Since the closed-form expressions of the parameters are not available, numerical approximation methods have been utilized for parameter estimation. Asymptotic confidence intervals are constructed within the likelihood framework. The percentile and Student-t bootstrap intervals are also proposed. In the Bayesian paradigm, independent informative and non-informative priors are assumed for the parameters, and the posterior point and interval inference have been carried out using the slice sampling algorithm. A discussion on choosing optimal monitoring intervals is also highlighted. A comprehensive simulation study is conducted to evaluate the performance of the proposed estimators across various censoring plans and sample sizes. A real data application illustrates the practical utility of the proposed methodologies. The results indicate that the Bayesian framework generally exhibits superior performance in both point and interval estimation.