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Biometrika 1971 58(3):677-678; doi:10.1093/biomet/58.3.677
© 1971 by Biometrika Trust
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MISCELLANEA

A neat way to prove asymptotic normality

JOHN HAIGH

University of Sussex

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

Key Words: Combinatorial central limit theorems • Nonparametric test statistics • Wilcoxon test • Kendall's rank correlation coefficient • Mann-Whitney test


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