Enhancing Overlap Measures in Censored Data Analysis: A Focus on Pareto Distributions and Adaptive Type-II Censoring

This article explores the application of the adaptive type-II progressive hybrid censoring scheme to calculate three widely recognized statistical measures of overlap for two Pareto distributions with distinct parameters. By utilizing this innovative censoring technique, we derive estimators for these measures and provide their asymptotic bias and variance. When small sample sizes pose challenges in assessing estimator precision or bias due to the lack of closed-form expressions for variances and exact sampling distributions, Monte Carlo simulations are employed to enhance reliability. Additionally, we construct confidence intervals for these measures using both the bootstrap method and Taylor approximation. Our approach offers improved accuracy and efficiency in estimating overlap measures, addressing key challenges in censored data analysis. To demonstrate the practical relevance of our proposed estimators, we include an illustrative application involving real data from an Iranian insurance company.