# 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.

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.

## Citations

2 citations in Web of Science®
2 citations in Scopus®