Abstract

In this paper we demonstrate a method for estimating asymptotic behavior of the regularly varying moments $E(K_\rho (X_n))$, $(n\to\infty)$ in the case of generalized Binomial Law. Here $K_\rho(x)$ is from the class of regularly varying functions in the sense of Karamata. We prove that $$ E(K_\rho(X_n))\sim K_\rho(E(X_n)), \ \rho>0, \ \ \ E(X_n)\to\infty \ \ \ (n\to\infty), $$ i.e., that the asymptotics of the first moment determines the behavior of all other moments.

MSC: 26A12

Pages:  31$-$36     

Volume  55 ,  Issue  1$-$2 ,  2003