Adaptive Type-II Progressive Hybrid Censoring and Its Impact on Rayleigh Data Overlap Estimation

This article uses the adaptive type-II progressive hybrid censoring scheme, first introduced by Ng et al. in 2009, to estimate the overlap of two Rayleigh distributions with distinct scale parameters. The estimators for these overlap measures are derived using this censoring method, and their asymptotic bias and variance are also provided. In cases where small sample sizes make it challenging to assess the precision or bias of the estimators due to the lack of closed-form expressions for variances and exact sampling distributions, Monte Carlo simulations are used. Additionally, confidence intervals for these measures are constructed using both the bootstrap method and Taylor approximation. To highlight the practical importance of our proposed estimators, we present an analysis of real-life data focusing on the effect of mercaptopurine on sustaining remission in patients with acute leukemia.