On the normal approximation of a sum of a random number of independent random variables

Abstract

In this paper, we extend the results obtained in [J. Sunklodas, Some estimates of normal approximation for the distribution of a sum of a random number of independent random variables, Lith. Math. J., 52(3):326–333, 2012] for a thrice-differentiable function h : R - R to the case of h [...] BL(R); namely, we estimate the quantity [...] where h is a real bounded Lipschitz function, Zn = (Sn - ESn) / [...], Sn = X1 + ... + Xn , X1, X2, ... are independent, not necessarily identically distributed, real random variables, N is a positive integer-valued r.v. independent of X1, X2, ..., and Y is a standard normal random variable.