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A FINITARY CHARACTERIZATION OF THE EWENS SAMPLING FORMULA

U. GARIBALDI

IMEM-CNR, c/o Department of Physics, University of Genoa, via Dodecaneso 33, Genoa, 16123, Italy

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D. COSTANTINI

National Cancer Research Institute (IST), Largo Benzi 10, Genoa, 16132, Italy

Department of Statistical Science, University of Bologna, via Belle Arti 41, Bologna, 40100, Italy

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P. VIARENGO

National Cancer Research Institute (IST), Largo Benzi 10, Genoa, 16132, Italy

Department of Statistical Science, University of Bologna, via Belle Arti 41, Bologna, 40100, Italy

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https://doi.org/10.1142/S0219525904000172Cited by:6 (Source: Crossref)

Abstract

The clustering of agents in the market is a typical problem dealt with in recent approaches to macroeconomic modeling, describing macroscopic variables in terms of the behavior of a large collection of microeconomic entities. Clustering is subject to many economic interpretations, often described by the Ewens Sampling Formula (ESF). In contrast with the usual complex derivations, 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 description of a system of n individuals considered as a closed system, a population, where individuals can change attributes over time. The probability is understood as the fraction of time the system spends in the considered partition. As the ESF represents an equilibrium distribution satisfying detailed balance, some properties difficult to prove are derived in a simple way. Besides the mean distribution of the cluster sizes, we study the probabilistic time behavior of clusters, in particular the mean survival as a function of the actual size and the correlation between size and age.

A shorter version of this paper was presented at the WEHIA 2003 conference, Kiel, May 2003.

Keywords:

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