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.

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