Barbour, A D (1992). On the binary expansion of a random integer. Statistics and Probability Letters, 14(3):235-241.
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.
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.
| 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: | 20 Feb 2018 13:03 |
| 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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Barbour, A D