Hostname: page-component-89b8bd64d-ksp62 Total loading time: 0 Render date: 2026-05-07T11:16:04.420Z Has data issue: false hasContentIssue false
  • English
  • Français

DETERMINING THE MODE FOR CONVOLUTION POWERS OF DISCRETE UNIFORM DISTRIBUTION

Published online by Cambridge University Press:  21 July 2011

Hacène Belbachir
Hacène Belbachir
Affiliation:
USTHB/Faculty of Mathematics, BP 32, El Alia, 16111 Bab Ezzouar, Algiers, Algeria E-mail: hbelbachir@usthb.dz; hacenebelbachir@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

We specify the smallest mode of the ordinary multinomials leading to the expression of the maximal probability of convolution powers of the discrete uniform distribution. The generating function for an extension of the maximal probability is given.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 25 , Issue 4 , October 2011 , pp. 469 - 475
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.Belbachir, H., Bouroubi, S., & Khelladi, A. (2008). Connection between ordinary multinomials, Fibonacci numbers, Bell polynomials and discrete uniform distribution. Annales de Mathematicae et Informaticae 35: 21–30.Google Scholar
2.Bertin, E.M.J. & Theodorescu, R. (1984). Some characterizations of discrete unimodality. Statistics and Probability Letters 2: 23–30.CrossRefGoogle Scholar
3.Brenti, F. (1994). Log-concave and unimodal sequences in algebra, combinatorics, and geometry: an update. Jerusalem combinatorics ’93, 71–89, Contemp. Math., 178, Amer. Math. Soc., Providence, RI.CrossRefGoogle Scholar
4.Comtet, L. (1970). Analyse combinatoire. Tomes I, II. Collection SUP: “Le Mathématicien”, 4, 5 Presses Universitaires de France, Paris.Google Scholar
5.Dharmadhikari, S. & Joak-Dev, K. (1988). Unimodality, convexity and applications. Boston: Academic Press.Google Scholar
6.de Moivre, A. (1967). The doctrine of chances, 3rd ed.New York: Chelsea Press.Google Scholar
7.de Moivre, A. (1731). Miscellanca analytica de scrichus et quadraturis. London: J. Tomson and J. Watts.Google Scholar
8.Mattner, L. & Roos, B. (2008). Maximal probabilities of convolution powers of discrete uniform distributions. Statistics and Probability Letters 78(17): pp. 2992–2996.CrossRefGoogle Scholar
9.Odlyzko, A.M. & Richmond, L.B. (1985). On the unimodality of high convolutions, Annals Probability, 13: 299–306.CrossRefGoogle Scholar
10.Siegmund-Schultze, R. & von Weizsäcker, H. (2007). Level crossing probabilities II: Polygonal recurrence of multidimensional random walks. Advances in Mathematics 208: 680–698.CrossRefGoogle Scholar
11.Stanley, R.P. (1989). Log-concave and unimodal sequences in algebra, combinatorics, and geometry. In graph theory and its applications: East and West (Jinan, 1986), New York: New York Academy of Science, pp. 500–535.Google Scholar
12.Wintner, A. (1938). Asymptotic distributions and infinite convolutions, Edwards Brothers, Ann. Arbor, Mich. University of California, Berkeley, California.Google Scholar