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Rounding of continuous random variables and oscillatory asymptotics
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2006 (English)In: Annals of Probability, ISSN 0091-1798, Vol. 34, no 5, 1807-1826 p.Article in journal (Refereed) Published
Abstract [en]

We study the characteristic function and moments of the integer-valued random variable [X + alpha], 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.

Place, publisher, year, edition, pages
2006. Vol. 34, no 5, 1807-1826 p.
Keyword [en]
Sheppard's correction, moments, characteristic function, Gumbel distribution, random assignment, digital search tree, Patricia trie
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URN: urn:nbn:se:uu:diva-22591DOI: 10.1214/009117906000000232ISI: 000242464000009OAI: oai:DiVA.org:uu-22591DiVA: diva2:50364
Available from: 2007-01-19 Created: 2007-01-19 Last updated: 2011-05-06Bibliographically approved

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Janson, Svante
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