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Limit theory of generalized order statistics
Faculty
Science
Year:
2007
Type of Publication:
Article
Pages:
1-11
Authors:
Barakat, H. M
DOI:
10.1016/j.jspi.2005.10.003
Journal:
JOURNAL OF STATISTICAL PLANNING AND INFERENCE ELSEVIER SCIENCE BV
Volume:
137
Research Area:
Mathematics
ISSN
ISI:000241099000001
Keywords :
week convergence, generalized order statistics, generalized extremes, generalized central order statistics, generalized quantiles, generalized intermediate order statistics
Abstract:
Generalized order statistics (gos) were introduced by Kamps {[}1995. A Concept of Generalized Order Statistics. Teubner, Stuttgart] to unify several models of ordered random variables (rv's), e.g., (ordinary) order statistics (oos), records, sequential order statistics (sos). In a wide subclass of gos that includes oos and sos, the possible limit distribution functions (df's) of the maximum gos are obtained in Nasri-Roudsari {[}1996. Extreme value theory of generalized order statistics. J. Statist. Plann. Inference 55, 281-297]. In this paper, for this subclass, necessary and sufficient conditions of weak convergence, as well as the form of the possible limit df's of extreme, intermediate and central gos are derived. These results are extended to a wider subclass. (c) 2005 Elsevier B.V. All rights reserved.
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