<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we study the limit distribution functions of the (lower-lower), (upper-upper) and (lower-upper) extreme and central-central <italic>m</italic>-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.</p></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.

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.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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...

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

Published Online: Dec 26, 2019

Page range: 525 - 532

Received: Dec 12, 2018

Accepted: Jul 23, 2019

DOI: https://doi.org/10.2478/prolas-2019-0080

Keywords
Gaussian sequences, weak convergence, random indices, generalised order statistics, bivariate generalised order statistics, generalised quasi-range

© 2019 Fatma Hashem Essawe et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Dec 26, 2019

Page range: 525 - 532

Received: Dec 12, 2018

Accepted: Jul 23, 2019

DOI: https://doi.org/10.2478/prolas-2019-0080

KeywordsGaussian sequences, weak convergence, random indices, generalised order statistics, bivariate generalised order statistics, generalised quasi-range

© 2019 Fatma Hashem Essawe et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Gaussian sequences, weak convergence, random indices, generalised order statistics, bivariate generalised order statistics, generalised quasi-range