Hostname: page-component-89b8bd64d-5bvrz Total loading time: 0 Render date: 2026-05-12T13:57:02.543Z Has data issue: false hasContentIssue false
  • English
  • Français

Strong unimodality

Published online by Cambridge University Press:  01 July 2016

Chris A. J. Klaassen
Chris A. J. Klaassen*
Affiliation:
University of Leiden
*
∗Postal address: Department of Mathematics and Computer Science, University of Leiden, Wassenaarseweg 80, Postbus 9512, 2300 RA Leiden, The Netherlands.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

It is proved that a distribution F is strongly unimodal iff any two quantiles of the convolution of F with any other distribution are further apart than the corresponding quantiles of F itself. Some related characterizations of strong unimodality are also given.

Keywords

SPREADCONVOLUTIONJENSEN’S INEQUALITY

Information

Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 17 , Issue 4 , December 1985 , pp. 905 - 907
Copyright
Copyright © Applied Probability Trust 1985 

References

Droste, W. and Wefelmeyer, W. (1985) A note on strong unimodality and dispersivity. J. Appl. Prob. 22, 235–239.CrossRefGoogle Scholar
Hewitt, E. and Stromberg, K. (1965) Real and Abstract Analysis. Springer-Verlag, Berlin.Google Scholar
Ibragimov, I. A. (1956) On the composition of unimodal distributions. Theory Prob. Appl. 1, 255–260.CrossRefGoogle Scholar
Lewis, T. and Thompson, J. W. (1981) Dispersive distributions, and the connection between dispersivity and strong unimodality. J. Appl. Prob. 18, 76–90.CrossRefGoogle Scholar
Lynch, J., Mimmack, G., and Proschan, F. (1983) Dispersive ordering results. Adv. Appl. Prob. 15, 889–891.CrossRefGoogle Scholar