Skip to main content
Log in

Order statistics of the generalised multinomial measure

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

We study certain order statistics with respect to (probability) mass distributions of multinomial type on the unit interval. The asymptotic behaviour of the average minimum and, respectively, maximum value among \(n\) words chosen independently at random with respect to the corresponding probability measure is analysed. This is done by a combination of a method based on the Mellin transform and the depoissonisation technique.

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

Access this article

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. Bassino, F., Prodinger, H.: \((q,\delta )\)-numeration systems with missing digits. Monatsh. für Math. 141, 89–99 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cristea, L.L., Prodinger, H.: Order statistics for the Cantor–Fibonacci distribution. Aequ. Math. 73, 78–91 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Flajolet, P., Gourdon, X., Dumas, P.: Mellin transforms and asymptotics: Harmonic sums. Theoret. Comput. Sci. 144, 3–58 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  4. Jacquet, P., Szpankowski, W.: Analytical de-Poissonization and its applications. Theoret. Comput. Sci. 201(1–2), 1–62 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  5. Okada, T., Sekiguchi, T., Shiota, Y.: A Generalization of Hata–Yamaguti’s results on the Takagi function II: multinomial case. Jpn. J. Indust. Appl. Math. 13, 435–463 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  6. Szpankowski, W.: Average case analysis of algorithms on sequences. Wiley-interscience series in discrete mathematics and optimization. Wiley, New York (with a foreword by Philippe Flajolet) (2001)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ligia L. Cristea.

Additional information

Communicated by A. Constantin.

This paper is dedicated to the memory of Philippe Flajolet who passed away on March 22, 2011.

L. L. Cristea was supported by the Austrian Science and Research Fund (FWF), Project P20412-N18.

H. Prodinger was supported by an incentive grant from the NRF.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cristea, L.L., Prodinger, H. Order statistics of the generalised multinomial measure. Monatsh Math 175, 333–346 (2014). https://doi.org/10.1007/s00605-014-0676-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00605-014-0676-5

Keywords

Mathematics Subject Classification

Navigation