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december 2019 Asymptotic Distributions of Record Values under Exponential Normalization
H. M. Barakat, E. M. Nigm, E. O. Abo Zaid
Bull. Belg. Math. Soc. Simon Stevin 26(5): 743-758 (december 2019). DOI: 10.36045/bbms/1579402820

Abstract

In this paper, we study the limit distribution of the record values under nonlinear normalization of the form $${\cal T}_n(x)=\exp\{u_{n}(| \log |x||)^{v_{n}}\mbox{sign}(\log |x|)\}\mbox{sign}(x),$$ which is called exponential norming ($e-$norming). The corresponding limit laws of the upper extremes are called $e$-max stable laws (denoted by $U(.)$). In this paper, we show that the limit distributions of the record values under exponential norming are of the form $ {\cal N}(-\log (-\log U(x))),$ where ${\cal N}(.)$ is the standard normal distribution. Moreover, we study the domains of attraction for these types of limit laws. Finally, some illustrative examples are given.

Citation

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H. M. Barakat. E. M. Nigm. E. O. Abo Zaid. "Asymptotic Distributions of Record Values under Exponential Normalization." Bull. Belg. Math. Soc. Simon Stevin 26 (5) 743 - 758, december 2019. https://doi.org/10.36045/bbms/1579402820

Information

Published: december 2019
First available in Project Euclid: 19 January 2020

zbMATH: 07167754
MathSciNet: MR4053851
Digital Object Identifier: 10.36045/bbms/1579402820

Subjects:
Primary: 60G70
Secondary: 60E05

Rights: Copyright © 2019 The Belgian Mathematical Society

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Vol.26 • No. 5 • december 2019
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