GAMMA-TYPE LIMIT DISTRIBUTION FOR EXTREME UNCENSORED ORDER STATISTICS UNDER RIGHT CENSORING - Dushatov N.T (TADQIQOTLAR, 2026)
Abstract. We study the asymptotic distribution of statistics constructed from extreme order statistics under random right censoring. Classical results show that, for complete samples, suitably normalized gaps between the minimum and maximum order statistics converge to a Gamma distribution with shape parameter two. However, such results generally fail when censoring is present and observed extrema are distorted. In this paper, we propose a censored-data–adapted statistic based on the smallest and largest uncensored observations. Under mild regularity conditions and assuming independent censoring, we prove that the proposed statistic converges in distribution to a Gamma distribution with shape parameter two. The result provides a theoretically justified extension of classical extreme-value limit theorems to right- censored data and can be implemented using standard survival analysis tools.