This article is cited in 3 papers

Asymptotic behavior of central order statistics under monotone normalization

E. I. Pancheva^a, A. Gacovska<sup>b

a</sup> Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
^b Ss Cyril and Methodius University of Skopje

Abstract: N. V. Smirnov [Tr. Mat. Inst. Steklova 25, 59 p. (1949; Zbl 0041.45301)] 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: $k$th upper order statistic; central rank; monotone normalization; regular norming sequence.

MSC: 62G30,60F05

Received: 31.07.2012

Language: English

DOI: 10.4213/tvp4499

 English version: Theory of Probability and its Applications, 2014, 58:1, 107–120

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