September 2013 Tail properties and asymptotic expansions for the maximum of the logarithmic skew-normal distribution
Xin Liao, Zuoxiang Peng, Saralees Nadarajah
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J. Appl. Probab. 50(3): 900-907 (September 2013). DOI: 10.1239/jap/1378401246

Abstract

We discuss tail behaviors, subexponentiality, and the extreme value distribution of logarithmic skew-normal random variables. With optimal normalized constants, the asymptotic expansion of the distribution of the normalized maximum of logarithmic skew-normal random variables is derived. We show that the convergence rate of the distribution of the normalized maximum to the Gumbel extreme value distribution is proportional to 1/(log n)1/2.

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Xin Liao. Zuoxiang Peng. Saralees Nadarajah. "Tail properties and asymptotic expansions for the maximum of the logarithmic skew-normal distribution." J. Appl. Probab. 50 (3) 900 - 907, September 2013. https://doi.org/10.1239/jap/1378401246

Information

Published: September 2013
First available in Project Euclid: 5 September 2013

zbMATH: 1293.62036
MathSciNet: MR3102524
Digital Object Identifier: 10.1239/jap/1378401246

Subjects:
Primary: 60G70 , 62E20
Secondary: 60F05 , 60F15

Keywords: extreme value distribution , logarithmic skew-normal distribution , Maximum , pointwise convergence rate , subexponentiality

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 3 • September 2013
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