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On the binary expansion of a random integer

Author

Listed:
  • Barbour, A. D.
  • Chen, L. H. Y.

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.

Suggested Citation

  • Barbour, A. D. & Chen, L. H. Y., 1992. "On the binary expansion of a random integer," Statistics & Probability Letters, Elsevier, vol. 14(3), pages 235-241, June.
    • Handle: RePEc:eee:stapro:v:14:y:1992:i:3:p:235-241
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