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Asymptotic behavior of the record values in a stationary Gaussian sequence, with applications

  • Haroon M. Barakat EMAIL logo and M. A. Abd Elgawad
From the journal Mathematica Slovaca

Abstract

In this paper, we study the limit distributions of upper and lower record values of a stationary Gaussian sequence under an equi-correlated set up. Moreover, the class of limit distribution functions (df’s) of the joint upper (and the lower) record values of a stationary Gaussian sequence is fully characterized. As an application of this result, the sufficient conditions for the weak convergence of the record quasi-range, record quasi-mid-range, record extremal quasi-quotient and record extremal quasi-product are obtained. Moreover, the classes of the non-degenerate limit df’s of these statistics are derived.

  1. Communicated by Gejza Wimmer

Acknowledgement

The authors would like to thank Professor Gejza Wimmer, as well as the anonymous referees for constructive suggestions and comments that lead to improvement of the readability of the paper.

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Received: 2018-05-03
Accepted: 2018-09-10
Published Online: 2019-05-21
Published in Print: 2019-06-26

© 2019 Mathematical Institute Slovak Academy of Sciences

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