The Annals of Probability

Rounding of continuous random variables and oscillatory asymptotics

Svante Janson

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Abstract

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.

Article information

Source
Ann. Probab., Volume 34, Number 5 (2006), 1807-1826.

Dates
First available in Project Euclid: 14 November 2006

Permanent link to this document
https://projecteuclid.org/euclid.aop/1163517225

Digital Object Identifier
doi:10.1214/009117906000000232

Mathematical Reviews number (MathSciNet)
MR2271483

Zentralblatt MATH identifier
1113.60017

Subjects
Primary: 60E05: Distributions: general theory 60F05: Central limit and other weak theorems
Secondary: 60C05: Combinatorial probability

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

Citation

Janson, Svante. Rounding of continuous random variables and oscillatory asymptotics. Ann. Probab. 34 (2006), no. 5, 1807--1826. doi:10.1214/009117906000000232. https://projecteuclid.org/euclid.aop/1163517225


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