A neat way to prove asymptotic normality

Abstract

SUMMARY An easy to use theorem for proving asymptotic normality, especially of combinatorial distributions, is proved, and illustrated by three neat applications. Harper (1967) used a new and appealing method to prove the asymptotic normality of the Stirling Numbers of the second kind. The purpose of this note is to extend his method slightly, and to use this extension to give brief proofs of three well-known results in nonparametric statistics. Harper's main theorem can be extracted as