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Asymptotic properties of random extremes under general normalization from nonidentical distributions
Faculty
Science
Year:
2004
Type of Publication:
Article
Pages:
275-287
Authors:
BARAKAT, HM, NIGM, EM, El-Adll, ME
DOI:
10.1007/s001840300284
Journal:
METRIKA PHYSICA-VERLAG GMBH \& CO
Volume:
59
Research Area:
Mathematics
ISSN
ISI:000221692500005
Keywords :
weak convergence, extremes, general nonlinear normalization, random sample size
Abstract:
In this paper we study the weak convergence of the generally normalized extremes (extremes under nonlinear monotone normalization) of random number of independent (nonidentically distributed) random variables. When the random sample size is assumed to converge in probability and the interrelation between the basic variables and their random size is not restricted, the limit forms as well as the sufficient conditions of convergence are derived. Moreover, when the random sample size is assumed to converge weakly and independent of the basic variables, the necessary and sufficient conditions for the convergence are derived.
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