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For a skew normal random sequence, convergence rates of the distribution of its partial maximum to the Gumbel extreme value distribution are derived. The asymptotic expansion of the distribution of the normalized maximum is given under an optimal choice of norming constants. We find that the optimal convergence rate of the normalized maximum to the Gumbel(More)
In this short note, we focus on the limiting behaviors of moments for normalized partial maxima of skew-normal samples. Under optimal norming constants, asymptotic expansions for moments of maxima of skew-normal samples are derived. These expansions are used to deduce convergence rates of moments of the normalized maxima to the moments of the corresponding(More)
Logarithmic general error distribution, an extension of the log-normal distribution , is proposed. Some interesting properties of the logarithmic general error distribution are derived. These properties are applied to establish the asymptotic behavior of the ratio of probability densities and the ratio of the tails of the logarithmic general error and(More)
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(More)
Suppose X1,X2, . . . are independent and identically distributed (iid) random variables with common distribution function (df) F. Let Mn =max{X1, . . . ,Xn} denote the maximum of the first n random variables and let w(F) = sup{x : F(x) < 1} denote the upper end point of F. The extreme value theory seeks norming constants an > 0, bn ∈ and a nondegenerate df(More)
Consider a triangular array of mean zero Gaussian random variables. Under some weak conditions this paper proves that the partial sums and the point processes of exceedances formed by the array are asymptotically independent. For a standardized stationary Gaussian sequence, it is shown under some mild conditions that the point process of exceedances formed(More)