Hostname: page-component-848d4c4894-jbqgn Total loading time: 0 Render date: 2024-06-14T00:44:11.872Z Has data issue: false hasContentIssue false
  • English
  • Français

A Poisson Approximation for an Occupancy Problem with Collisions

Part of: Combinatorial probability

Published online by Cambridge University Press:  14 July 2016

Toshio Nakata
Toshio Nakata*
Affiliation:
Fukuoka University of Education
*
∗Postal address: Department of Mathematics, Fukuoka University of Education, Akama-Bunkyomachi, Munakata, Fukuoka, 811-4192, Japan. Email address: nakata@fukuoka-edu.ac.jp
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.

We study collision probabilities concerning the simple balls-and-bins problem developed by Wendl (2003). In this article we give the factorial moment of the number of collisions. Moreover, we obtain a Poisson approximation for the number of collisions using the Chen-Stein method.

Keywords

Collision probabilityoccupancy problemPoisson approximationChen-Stein method

MSC classification

Secondary: 60C05: Combinatorial probability
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 2 , June 2008 , pp. 430 - 439
Copyright
Copyright © Applied Probability Trust 2008 

References

[1] Alon, N. and Spencer, J. (2000). The Probabilistic Method, 2nd edn. John Wiley, New York.CrossRefGoogle Scholar
[2] Arratia, R., Goldstein, L. and Gordon, L. (1990). Poisson approximation and the Chen–Stein method. Statist. Sci. 5, 403–434.Google Scholar
[3] Barbour, A. D., Holst, L. and Janson, S. (1992). Poisson Approximation. Oxford University Press.Google Scholar
[4] Durrett, R. (1996). Probability: Theory and Examples, 2nd edn. Duxbury Press, Belmont, CA.Google Scholar
[5] Flajolet, P. and Sedgewick, R. (2008). Analytic Combinatorics. Cambridge University Press.Google Scholar
[6] Grimmett, G. and Stirzaker, D. (2001). Probability and Random Processes, 3rd edn. Oxford University Press.CrossRefGoogle Scholar
[7] Janson, S., Łuczak, T. and Ruciński, A. (2000). Random Graphs. John Wiley, New York.CrossRefGoogle Scholar
[8] Johnson, N. L. and Kotz, S. (1977). Urn Models and Their Application. John Wiley, New York.Google Scholar
[9] Knuth, D. (1973). The Art of Computer Programming, Fundamental Algorithms, Vol. 1, 3rd edn. Addison-Wesley, Reading, MA.Google Scholar
[10] Kolchin, F., Sevastyanov, A. and Chistyakov, P. (1978). Random Allocations. John Wiley, New York.Google Scholar
[11] Krivelevich, M., and Nachmias, A. (2006). Coloring complete bipartite graphs from random lists. Random Structures Algorithms 29, 436–449.CrossRefGoogle Scholar
[12] Nakata, T. (2008). Collision probability for an occupancy problem. To appear in Statist. Prob. Lett. Google Scholar
[13] Ross, S. (1996). Stochastic Processes, 2nd edn. John Wiley, New York.Google Scholar
[14] Wendl, M. (2003). Collision probability between sets of random variables. Statist. Prob. Lett. 64, 249–254.CrossRefGoogle Scholar
[15] Wendl, M. (2005). Probabilistic assessment of clone overlaps in DNA fingerprint mapping via a priori models. J. Comput. Biol. 12, 283–297.CrossRefGoogle ScholarPubMed