Open AccessLimit Theorems for Bivariate Generalised Order Statistics in Stationary Gaussian Sequences with Random Sample Sizes
Author(s) -
Fatma Hashem Essawe,
M. A. Abd Elgawad,
H. M. Barakat,
Hui Zhao
Publication year - 2019
Publication title -
proceedings of the latvian academy of sciences. section b, natural sciences/latvijas zinātņu akadēmijas vēstis. a daļa, humanitārās un sociālās zinātnes
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.168
H-Index - 9
eISSN - 2255-890X
pISSN - 1407-009X
DOI - 10.2478/prolas-2019-0080
Subject(s) - mathematics , bivariate analysis , statistics , gaussian , order statistic , limit (mathematics) , stationary sequence , central limit theorem , range (aeronautics) , random variable , convergence of random variables , weak convergence , mathematical analysis , physics , materials science , computer security , quantum mechanics , computer science , composite material , asset (computer security)
In this paper, we study the limit distribution functions of the (lower-lower), (upper-upper) and (lower-upper) extreme and central-central m -generalised order statistics (m–GOS) of stationary Gaussian sequences under an equi-correlated set up, when the random sample size is assumed to converge weakly and independent of the basic variables. Moreover, sufficient conditions for a weak convergence of generalised quasi-range with random indices are obtained.