Asymptotic expansions for sums of nonidentically distributed Bernoulli random variables

Abstract

This paper concerns an asymptotic expansion for the distribution of the sum of independent zero-one random variables in case where this surn has variance σ n 2 → ∞. The expansion presented is given to the order O( σ n −2). An application to the study of the exact rate of convergence in the central limit theorem for intermediate order statistics is included.