Limit Theorems for Bivariate Generalised Order Statistics in Stationary Gaussian Sequences with Random Sample Sizes | Zendy

Fatma Hashem Essawe | Zendy; Mohamed A. Abd Elgawad | Zendy; H. M. Barakat | Zendy; Hui Zhao | Zendy

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Limit Theorems for Bivariate Generalised Order Statistics in Stationary Gaussian Sequences with Random Sample Sizes

Author(s) -

Fatma Hashem Essawe,

Mohamed A. Abd Elgawad,

H. M. Barakat,

Hui Zhao

Publication year - 2019

Publication title -

proceedings of the latvian academy of sciences section b natural exact and applied sciences

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.

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