Berry-Esseen Bounds for Random Sums of Non-i.i.d. Random Variables

Let (Xn) be a sequence of independent random variables and N a positive integral-valued random variable such that N,X1,X2,... are independent. In 2008, N.Chaidee and K.Neammenee [10] gave Berry-Esseen bounds for random sums in the case of X1,X2,... are identically distributed random variables by using Stein’s method. In this work, we use the technique from [10] to establish the Berry-Esseen bounds without assuming the identical distributions of X1,X2,...