Tail Properties and Asymptotic Expansions for the Maximum of the Logarithmic Skew-Normal Distribution

We discuss tail behaviors, subexponentiality and 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. It shows 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.