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
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
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