Generalized binomial law and regularly varying moments

Abstract

In this paper we demonstrate a method for estimating asymptotic behavior of the regularly varying moments E(Kρ(Xn)), (n → ∞) in the case of generalized Binomial Law. Here Kρ(x) is from the class of regularly varying functions in the sense of Karamata. We prove that E(Kρ(Xn)) ∼ Kρ(E(X n)), ρ > 0, E(Xn) → ∞ (n → ∞), i.e., that the asymptotics of the first moment determines the behavior of all other moments.