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.

Let {X n (t), t∈[0,∞)}, n∈ℕ, be standard stationary Gaussian processes. The limit distribution of t∈[0,T(n)]|Xn (t)| is established as r n (t), the correlation function of {X n (t), t∈[0,∞)}, n∈ℕ, which satisfies the local and long-range strong dependence conditions, extending the results obtained in Seleznjev (1991).

Let {X n , n ≥ 1} be an independent, identically distributed random sequence with each X n having the general error distribution. In this paper we derive the exact uniform convergence rate of the distribution of the maximum to its extreme value limit.

An almost sure limit theorem for the maxima of multivariate stationary Gaussian sequences is proved under some mild conditions.