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September 2006 Rounding of continuous random variables and oscillatory asymptotics
Svante Janson
Ann. Probab. 34(5): 1807-1826 (September 2006). DOI: 10.1214/009117906000000232


We study the characteristic function and moments of the integer-valued random variable ⌊X+α⌋, where X is a continuous random variables. The results can be regarded as exact versions of Sheppard’s correction. Rounded variables of this type often occur as subsequence limits of sequences of integer-valued random variables. This leads to oscillatory terms in asymptotics for these variables, something that has often been observed, for example in the analysis of several algorithms. We give some examples, including applications to tries, digital search trees and Patricia tries.


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Svante Janson. "Rounding of continuous random variables and oscillatory asymptotics." Ann. Probab. 34 (5) 1807 - 1826, September 2006.


Published: September 2006
First available in Project Euclid: 14 November 2006

zbMATH: 1113.60017
MathSciNet: MR2271483
Digital Object Identifier: 10.1214/009117906000000232

Primary: 60E05 , 60F05
Secondary: 60C05

Keywords: Characteristic function , digital search tree , Gumbel distribution , moments , Patricia trie , random assignment , Sheppard’s correction

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 5 • September 2006
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