Asymptotic behavior of central order statistics under monotone normalization - Pancheva, E.I. Gacovska, A. (Elsevier, SIAM, 2014)
Smirnov [Trudy Mat. Inst. Steklov., 25 (1949), pp. 3-60 (in Russian); Amer. Math. Transl., 67 (1952) (in English)] derived four limit types of distributions for linearly normalized central order statistics under the weak convergence. In this paper we investigate the possible limit distributions of the kth upper order statistics with central rank using monotone regular norming sequences and obtain 13 possible types.
Keywords: Central rank, k-th upper order statistic, Monotone normalization, Regular norming sequence