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

Fatma Hashem Essawe; Mohamed Abd Elgawad; Haroon Mohamed Barakat; Hui Zhao

doi:10.2478/prolas-2019-0080

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

Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences.

Volume 73 (2019): Issue 6 (December 2019)

By: Fatma Hashem Essawe, Mohamed Abd Elgawad, Haroon Mohamed Barakat and Hui Zhao

Open Access

|Dec 2019

Abstract

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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Articles in this issue

DOI: https://doi.org/10.2478/prolas-2019-0080 | Journal eISSN: 2255-890X | Journal ISSN: 1407-009X

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Language: English

Page range: 525 - 532

Submitted on: Dec 12, 2018

Accepted on: Jul 23, 2019

Published on: Dec 26, 2019

Published by: Latvian Academy of Sciences

In partnership with: Paradigm Publishing Services

Publication frequency: 6 issues per year

Keywords:

Gaussian sequences,

weak convergence,

random indices,

generalised order statistics,

bivariate generalised order statistics,

generalised quasi-range

Related subjects:

General interest,

Mathematics,

General mathematics

© 2019 Fatma Hashem Essawe, Mohamed Abd Elgawad, Haroon Mohamed Barakat, Hui Zhao, published by Latvian Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 73 (2019): Issue 6 (December 2019)