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On generalized Pólya urn models

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  • Kotz, Samuel
  • Mahmoud, Hosam
  • Robert, Philippe

Abstract

We consider a general two-color urn model characterized by a 2x2 matrix of integerswithout constraints on the values of these four integers other than non-negativity. Exact distributions of the number of balls of a specific color that appear after n draws are presented. Via Poissonization, we obtain an asymptotic mean for a specific example to illustrate that asymptotics of bona fide nature may appear in non-classical urn models.

Suggested Citation

  • Kotz, Samuel & Mahmoud, Hosam & Robert, Philippe, 2000. "On generalized Pólya urn models," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 163-173, August.
    • Handle: RePEc:eee:stapro:v:49:y:2000:i:2:p:163-173
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    References listed on IDEAS

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    1. Gouet, Raúl, 1989. "A martingale approach to strong convergence in a generalized Pólya-Eggenberger urn model," Statistics & Probability Letters, Elsevier, vol. 8(3), pages 225-228, August.
    2. Smythe, R. T., 1996. "Central limit theorems for urn models," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 115-137, December.
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    Cited by:

    1. Franchini, Simone, 2017. "Large deviations for generalized Polya urns with arbitrary urn function," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3372-3411.
    2. Janson, Svante, 2004. "Functional limit theorems for multitype branching processes and generalized Pólya urns," Stochastic Processes and their Applications, Elsevier, vol. 110(2), pages 177-245, April.

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