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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: [email protected]
Thierry Huillet
Affiliation:
Laboratoire de Physique Théorique et Modélisation, CNRS-UMR 8089 et Université de Cergy-Pontoise, Neuville sur Oise, France, E-mail: [email protected]
Christian Paroissin
Affiliation:
MODAL'X, Université de Paris 10 Nanterre, 92001 Nanterre Cédex, France, E-mail: [email protected]
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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.

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

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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.