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Limit theory for joint generalized order statistics
REVSTAT – Statistical Journal • 2014
Publication Information
Authors
H. M. Abd Elgawad
Keywords
• generalized order statistics; generalized extreme order statistics; generalized central order statistics; generalized intermediate order statistics.
Journal
REVSTAT – Statistical Journal
Publisher
Not Available
Volume
Volume 12, Number 3, November 2014
Issue
Not Available
Pages
199-220
publication.type
International
Paper Link
Not Available
Supplementary Materials
Not Available
Abstract
In Kamps [7] generalized order statistics (gos) have been introduced as a unifying
theme for several models of ascendingly ordered random variables (rv’s). The main
aim of this paper is to study the limit joint distribution function (df) of any two
statistics in a wide subclass of the gos model known as m-gos. This subclass contains
many important practical models of gos such as ordinary order statistics (oos), order
statistics with non-integer sample size, and sequential order statistics (sos). The
limit df’s of lower-lower extreme, upper-upper extreme, lower-upper extreme, centralcentral
and lower-lower intermediate m-gos are obtained. It is revealed that the
convergence of the marginals m-gos implies the convergence of the joint df. Moreover, the conditions, under which the asymptotic independence between the two marginalsoccurs, are derived.
theme for several models of ascendingly ordered random variables (rv’s). The main
aim of this paper is to study the limit joint distribution function (df) of any two
statistics in a wide subclass of the gos model known as m-gos. This subclass contains
many important practical models of gos such as ordinary order statistics (oos), order
statistics with non-integer sample size, and sequential order statistics (sos). The
limit df’s of lower-lower extreme, upper-upper extreme, lower-upper extreme, centralcentral
and lower-lower intermediate m-gos are obtained. It is revealed that the
convergence of the marginals m-gos implies the convergence of the joint df. Moreover, the conditions, under which the asymptotic independence between the two marginalsoccurs, are derived.