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Limit distributions of random record model in a stationary Gaussian sequence
COMMUNICATIONS IN STATISTICS—THEORY AND METHODS • 2019
Publication Information
Authors
M. A. Abd Elgawad, H. M. Barakat & S. Xiong
Keywords
Gaussian sequences; record
values; joint record values;
random record model;
random record functions
Journal
COMMUNICATIONS IN STATISTICS—THEORY AND METHODS
Publisher
Taylor and Francis
Volume
https://doi.org/10.1080/03610926.2018.1554131
Issue
Not Available
Pages
Not Available
publication.type
International
Paper Link
Not Available
Supplementary Materials
Not Available
Abstract
We study the limit distributions of upper and lower record values of
a stationary Gaussian sequence (SGS) under an equi-correlated set
up, when the random sample size is assumed to converge weakly
and independent of the basic variables. Moreover, the class of limit
distribution functions (df’s) of joint upper and lower record values of
a SGS with random indices are fully characterized. As an application of this result, the sufficient conditions for the weak convergence of record quasi-range, record quasi-mid-range, record extremal quasiquotient and record extremal quasi-product with random indices are obtained. Moreover, the classes of the non degenerate limit df’s of these statistics are derived.
a stationary Gaussian sequence (SGS) under an equi-correlated set
up, when the random sample size is assumed to converge weakly
and independent of the basic variables. Moreover, the class of limit
distribution functions (df’s) of joint upper and lower record values of
a SGS with random indices are fully characterized. As an application of this result, the sufficient conditions for the weak convergence of record quasi-range, record quasi-mid-range, record extremal quasiquotient and record extremal quasi-product with random indices are obtained. Moreover, the classes of the non degenerate limit df’s of these statistics are derived.