Upper-bound estimates for weighted sums satisfying Cramer’s condition

Abstract

Let S = ω₁S₁ + ω₂S₂ + ⋯ + ω_NS_N. Here S_j is the sum of identically distributed random variables and ω_j  > 0 denotes weight. We consider the case, when S_j  is the sum of independent random variables satisfying Cramer’s condition. Upper-bounds for the accuracy of compound Poisson first and second order approximations in uniformmetric are established.