Skip to main content
SpringerLink
Log in

On Extreme Values of the Rényi Entropy under Coupling of Probability Distributions

  • Information Theory
  • Published:
Problems of Information Transmission Aims and scope Submit manuscript

Abstract

We consider the problem of determining extreme values of the Rényi entropy for a discrete random variable provided that the value of the α-coupling for this random variable and another one with a given probability distribution is fixed.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Rényi, A., On Measures of Entropy and Information, Proc. 4th Berkeley Sympos. on Mathematical Statistics and Probability, Berkely, CA, USA, June 20–July 30, 1960, Neyman, J., Ed., Berkely: Univ. of California Press, 1961, vol. 1: Contributions to the Theory of Statistics, pp. 547–561.

    Google Scholar 

  2. Aczél, J. and Daróczy, Z., On Measures of Information and Their Characterization, New York: Academic, 1975.

    MATH  Google Scholar 

  3. Prelov, V.V., On One Extreme Value Problem for Entropy and Error Probability, Probl. Peredachi Inf., 2014, vol. 50, no. 3, pp. 3–18 [Probl. Inf. Transm. (Engl. Transl.), 2014, vol. 50, no. 3, pp. 203–216].

    MathSciNet  MATH  Google Scholar 

  4. Ho, S.-W. and Yeung, R.W., The Interplay between Entropy and Variational Distance, IEEE Trans. Inform. Theory, 2010, vol. 56, no. 12, pp. 5906–5929.

    Article  MathSciNet  MATH  Google Scholar 

  5. Marshall, A.W., Olkin, I., and Arnold, B.C., Inequalities: Theory of Majorization and Its Applications, New York: Springer, 2011.

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    V. V. Prelov

Authors
  1. V. V. Prelov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Prelov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Prelov, V.V. On Extreme Values of the Rényi Entropy under Coupling of Probability Distributions. Probl Inf Transm 55, 46–52 (2019). https://doi.org/10.1134/S0032946019010022

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0032946019010022

Search

Navigation