Abstract
This article delves into the examination of the adaptive type-II progressive hybrid censoring scheme, originally introduced by Ng et al. in [22]. This censoring method is employed to make inferences about three widely recognized measures of overlap: Matusita’s measure (denoted as \(\rho\) ), Morisita’s measure (represented as \(\lambda\) ), and Weitzman’s measure ( \(\Delta\) ) for two Burr XII distributions with distinct parameters. We derive the asymptotic bias and variance of the estimators for these overlap measures. In cases where limited sample sizes make it challenging to ascertain the precision or bias of these estimators due to the absence of closed-form expressions for their variances and exact sampling distributions, we resort to Monte Carlo simulations. Additionally, confidence intervals for these measures are constructed using both the bootstrap method and Taylor approximation. To underscore the practical significance of our proposed estimators, we provide an illustrative application by analyzing head and neck cancer data.
