On the binary expansion of a random integer

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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Year of publication:	1992
Authors:	Barbour, A. D. ; Chen, L. H. Y.
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 14.1992, 3, p. 235-241
Publisher:	Elsevier
Keywords:	Random integer binary expansion Stein's method binomial mixtures

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005138351