Long-run Behavior of Macroeconomic Models with Heterogeneous Agents: Asymptotic Behavior of One- and Two-Parameter Poisson-Dirichlet Distributions
This paper discusses a symptotic behavior of one-and two-parameter Poisson-Dirichlet models, that is, Ewens models and its two parameter extensions by Pitman, and show that their a symptotic behavior arevery different. The paper shows asymptotic properties of a class of one-and two-parameter Poisson-Dirichlet distribution models are drastically different. Convergence behavioris expressedin termsof generalized Mittag-Leffler distributions in the statistics literature. The coefficients of variations of suitably normalized number of clusters andof clusters of specific sizesdo not vanish in the two-parameter version, but they do in one-parameter Ewens models.
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