Journal of Applied Probability

Tail properties and asymptotic expansions for the maximum of the logarithmic skew-normal distribution

Xin Liao, Zuoxiang Peng, and Saralees Nadarajah

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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.

Article information

J. Appl. Probab., Volume 50, Number 3 (2013), 900-907.

First available in Project Euclid: 5 September 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62E20: Asymptotic distribution theory 60G70: Extreme value theory; extremal processes
Secondary: 60F15: Strong theorems 60F05: Central limit and other weak theorems

Extreme value distribution logarithmic skew-normal distribution maximum pointwise convergence rate subexponentiality


Liao, Xin; Peng, Zuoxiang; Nadarajah, Saralees. Tail properties and asymptotic expansions for the maximum of the logarithmic skew-normal distribution. J. Appl. Probab. 50 (2013), no. 3, 900--907. doi:10.1239/jap/1378401246.

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