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.