Hostname: page-component-89b8bd64d-4ws75 Total loading time: 0 Render date: 2026-05-07T09:33:42.074Z Has data issue: false hasContentIssue false
  • English
  • Français

SIZE-BIASED PERMUTATION OF DIRICHLET PARTITIONS AND SEARCH-COST DISTRIBUTION

Published online by Cambridge University Press:  01 January 2005

Javiera Barrera ,
Thierry Huillet  and
Christian Paroissin
Javiera Barrera
Affiliation:
Departmento Ingeniería Matemática and Centro Modelamiento Matemático, UMR 2071 UCHILE-CNRS, Santiago, Chile, E-mail: barrera@dim.uchile.cl
Thierry Huillet
Affiliation:
Laboratoire de Physique Théorique et Modélisation, CNRS-UMR 8089 et Université de Cergy-Pontoise, Neuville sur Oise, France, E-mail: huillet@ptm.u-cergy.fr
Christian Paroissin
Affiliation:
MODAL'X, Université de Paris 10 Nanterre, 92001 Nanterre Cédex, France, E-mail: cparoiss@u-paris10.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Consider the random Dirichlet partition of the interval into n fragments at temperature θ > 0. Explicit results on the law of its size-biased permutation are first supplied. Using these, new results on the comparative search cost distributions from Dirichlet partition and from its size-biased permutation are obtained.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 19 , Issue 1 , January 2005 , pp. 83 - 97
Copyright
© 2005 Cambridge University Press

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

REFERENCES

Barrera, J. & Paroissin, C. (2004). On the distribution of the stationary search cost for the move-to-front rule with random weights. Journal of Applied Probability 41(1): 250–262.Google Scholar
Burville, P.J. & Kingman, J.F.C. (1973). On a model of storage and search. Journal of Applied Probability 10: 697–701.Google Scholar
Collet, P., Huillet, T., & Martinez, S. (2003). Size-biased picking for finite random partitions of the interval. Preprint; Journal of Applied Probability (submitted).Google Scholar
Donnelly, P. (1986). Partition structures, Pòlya urns, the Ewens sampling formula and the age of alleles. Theoretical Population Biology 30: 271–288.Google Scholar
Donnelly, P. (1991). The heaps process, libraries and size-biased permutation. Journal of Applied Probability 28: 321–335.Google Scholar
Engen, S. (1978). Stochastic abundance models. Monographs on Applied Probability and Statistics. London: Chapman & Hall.
Ewens, W.J. (1990). Population genetics theory—the past and the future. In S. Lessard (ed.), Mathematical and statistical developments of evolutionary theory. Dordrecht: Kluwer.
Feller, W. (1971). An introduction to probability theory and its applications, Vol. 2, 2nd ed. New York: Wiley.
Fill, J.A. (1996). Limits and rates of convergence for the distribution of search cost under the move-to-front rule. Theoretical Computer Science 164: 185–206.Google Scholar
Fill, J. A. & Holst, L. (1996). On the distribution of search cost for the move-to-front rule. Random Structures and Algorithms 8(3): 179–186.Google Scholar
Flajolet, P., Gardy, D., & Thimonier, L. (1992). Birthday paradox, coupon collectors, caching algorithms and self-organizing search. Discrete Applied Mathematics 39: 207–229.Google Scholar
Hawkes, J. (1981). On the asymptotic behaviour of sample spacings. Mathematical Proceedings of the Cambridge Philosophical Society 90(2): 293–303.Google Scholar
Hildebrand, M. (1999). On a conjecture of Fill and Holst involving the move-to-front rule and cache faults. Probability in the Engineering and Informational Sciences 13(3): 377–385.Google Scholar
Kingman, J.F.C. (1975). Random discrete distributions. Journal of the Royal Statistical Society. Series B 37: 1–22.Google Scholar
Kingman, J.F.C. (1978). Random partitions in population genetics. Proceedings of the Royal Society London Series A 361(1704): 1–20.Google Scholar
Kingman, J.F.C. (1993). Poisson processes. Oxford: Clarendon Press.
Patil, G.P. & Taillie, C. (1977). Diversity as a concept and its implications for random environments. Bulletin de l'Institut International de Statistique 4: 497–515.Google Scholar
Tavaré, S. & Ewens, W.J. (1997). Multivariate Ewens distribution. In N.L. Johnson, S. Kotz, & N. Balakrishnan (eds.), Discrete multivariate distributions. New York: Wiley, pp. 232–246.