## Journal of Applied Probability

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

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

Xin Liao, Zuoxiang Peng, and Saralees Nadarajah

#### 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}.

#### Article information

**Source**

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

**Dates**

First available in Project Euclid: 5 September 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.jap/1378401246

**Digital Object Identifier**

doi:10.1239/jap/1378401246

**Mathematical Reviews number (MathSciNet)**

MR3102524

**Zentralblatt MATH identifier**

1293.62036

**Subjects**

Primary: 62E20: Asymptotic distribution theory 60G70: Extreme value theory; extremal processes

Secondary: 60F15: Strong theorems 60F05: Central limit and other weak theorems

**Keywords**

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

#### Citation

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. https://projecteuclid.org/euclid.jap/1378401246