GAMMA-TYPE LIMIT DISTRIBUTION FOR EXTREME UNCENSORED ORDER STATISTICS UNDER RIGHT CENSORING
Keywords:
Keywords. Right censoring; order statistics; extreme values; Gamma distribution; asymptotic distribution.Abstract
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.
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