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On the binary expansion of a random integer


Barbour, A D (1992). On the binary expansion of a random integer. Statistics and Probability Letters, 14(3):235-241.

Abstract

It is shown that the distribution of the number of ones in the binary expansion of an integer chosen uniformly at random from the set 0, 1,…, n − 1 can be approximated in total variation by a mixture of two neighbouring binomial distributions, with error of order (log n)−1. The proof uses Stein's method.

Abstract

It is shown that the distribution of the number of ones in the binary expansion of an integer chosen uniformly at random from the set 0, 1,…, n − 1 can be approximated in total variation by a mixture of two neighbouring binomial distributions, with error of order (log n)−1. The proof uses Stein's method.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Random integer, binary expansion, Stein's method, binomial mixtures
Language:English
Date:1992
Deposited On:12 Apr 2010 15:06
Last Modified:24 Sep 2019 16:19
Publisher:Elsevier
ISSN:0167-7152
OA Status:Closed
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/0167-7152(92)90028-4
Related URLs:http://user.math.uzh.ch/barbour/pub/Barbour/BChen_Binary.pdf (Author)

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