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

Xin Liao, Zuoxiang Peng, Saralees Nadarajah

• 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)½.