Skip to main content
SpringerLink
Log in

Tutorial on large deviations for the binomial distribution

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

We present, in an easy to use form, the large deviation theory of the binomial distribution: how to approximate the probability ofk or more successes inn independent trials, each with success probabilityp, when the specified fraction of successes,a≡k/n, satisfies 0<p<a<1.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature

  • Arratia, R., L. Goldstein and L. Gordon. 1989. “Two Moments Suffice for Poisson Approximations: the Chen-Stein Method.” To appear inAnn. Probability.

  • Arratia, R., and E. Lander. 1988. “The Distribution of Clusters in Random Graphs.” Preprint. Bahadur, R. H. 1971. “Some Limit Theorems in Statistics.” SIAM Regional Conference Series in Applied Mathematics, Vol. 4.

  • —, and R. Ranga Rao. 1960. “On Deviations of the Sample Mean.”Ann. Math. Statist. 31, 1015–1027.

    MathSciNet  Google Scholar 

  • H. Cramer. 1938. “Sur un Nouveaux Theoreme-Limite de la Theorie des Probabilities.” Actualites Scientifiques et Industrielles; Colloque consacre a la Theorie des Probabilites. Vol. 3, No. 736, pp. 5–23. Paris: Hermann.

    Google Scholar 

  • Ellis, R. S. 1985.Entropy, Large Deviations, and Statistical Mechanics. Berlin Springer.

    Google Scholar 

  • Feller, W. 1968.An Introduction to Probability Theory and its Applications. Vol. 1. New York: Wiley.

    Google Scholar 

  • Varadhan, S. R. S. 1984. “Large Deviations and Applications.” SIAM Regional Conference Series in Applied Mathematics, Vol. 46.

  • Waterman, M. S., R. Arratia and D. Galas. 1984. Pattern Recognition in Several Sequences: Consensus and Alignment.Bull. Math. Biol. 46, 515–527.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Southern California, 90089, Los Angeles, CA, U.S.A.

    R. Arratia & L. Gordon

Authors
  1. R. Arratia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Gordon
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by NIH grant GM 36230 and NSF grant DMS 8601986.

Supported by NIH grant GM 36230 and a grant from the System Development Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arratia, R., Gordon, L. Tutorial on large deviations for the binomial distribution. Bltn Mathcal Biology 51, 125–131 (1989). https://doi.org/10.1007/BF02458840

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02458840

Keywords

Search

Navigation