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A Finitary Characterization of the Ewens Sampling Formula

In: Nonlinear Dynamics and Heterogeneous Interacting Agents

Author

Listed:
  • Domenico Costantini

    (National Cancer Research Institute (1ST), Genoa)

  • Ubaldo Garibaldi

    (University of Genoa, Italy)

  • Paolo Viarengo

    (National Cancer Research Institute (1ST), Genoa
    University of Bologna)

Abstract

Summary The clustering of agents in the market is a typical problem dealt with by the new approaches to macroeconomic modeling, describing macroscopic variables in terms of the behavior of a large collection of microeconomic entities. Clustering has many economic interpretations [3], that are often described by Ewens' Sampling Formula (ESF). This formula can be traced back to Fisher as “species sampling”, and its main use was restricted to genetics for a long time. Contrary to the usual complex derivations [18], we suggest a finitary characterization of the ESF pointing to real economic processes. Our approach is finitary in the sense that we provide a probabilistic characterisation of a system of n individuals considered as a closed system, a population, where individuals can change attributes as time moves on. The intuitive meaning of the probability is the fraction of time the system spends in the considered partition. As ESF represents an equilibrium distribution satisfying detailed balance, some properties which are otherwise difficult to prove are derived in a simple way.

Suggested Citation

  • Domenico Costantini & Ubaldo Garibaldi & Paolo Viarengo, 2005. "A Finitary Characterization of the Ewens Sampling Formula," Lecture Notes in Economics and Mathematical Systems, in: Thomas Lux & Eleni Samanidou & Stefan Reitz (ed.), Nonlinear Dynamics and Heterogeneous Interacting Agents, pages 221-236, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-27296-0_15
    DOI: 10.1007/3-540-27296-8_15
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    Citations

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    Cited by:

    1. U. Garibaldi & D. Costantini & P. Viarengo, 2007. "The two-parameter Ewens distribution: a finitary approach," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 2(2), pages 147-161, December.
    2. Scalas, Enrico & Gallegati, Mauro & Guerci, Eric & Mas, David & Tedeschi, Alessandra, 2006. "Growth and allocation of resources in economics: The agent-based approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 86-90.

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