Institute of Mathematics

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    Asymptotic behavior of central order statistics under monotone normalization
    (Elsevier, SIAM, 2014)
    Pancheva, E.I. Gacovska, A.
    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.
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    Randomly Indexed Central Order Statistics
    (Bulgarian Academy of Sciences, 2013)
    Gacovska, Aneta Pancheva, Elisaveta I.
    In our paper from 2012 we have considered the upper order statistics with central rank of sample with deterministic size. Here we investigate the asymptotic behaviour of randomly indexed upper order statistics using regular norming time-space changes.