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April, 1967 Stirling Behavior is Asymptotically Normal
L. H. Harper
Ann. Math. Statist. 38(2): 410-414 (April, 1967). DOI: 10.1214/aoms/1177698956


The Stirling numbers $\{\sigma_n^j\}$ of the second kind are asymptotically normal. This result is similar to results achieved by Feller [1] and Goncarov [2] for other combinatorial distributions. Here the technique of proof is different; one of the most general forms of the central limit theorem is used. Interesting qualitative information about the Stirling numbers is also obtained from this result. Asymptotic estimates on the value of $\max_j \{\sigma^j_n\}$ are given.


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L. H. Harper. "Stirling Behavior is Asymptotically Normal." Ann. Math. Statist. 38 (2) 410 - 414, April, 1967.


Published: April, 1967
First available in Project Euclid: 27 April 2007

zbMATH: 0154.43703
MathSciNet: MR211432
Digital Object Identifier: 10.1214/aoms/1177698956

Rights: Copyright © 1967 Institute of Mathematical Statistics

Vol.38 • No. 2 • April, 1967
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