This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the n partitions of the interval [0, Wn] are independent and identically distributed random variables following the generalized Mittag-Leffler distribution. The expected value and variance of the one-dimensional marginal are derived as well as the form of its probability density function. A related generalized Dirichlet distribution is studied that provides a reasonable approximation for some values of the parameters. The relation between this distribution and other generalizations of the Dirichlet distribution is discussed. Monte Carlo simulations of the one-dimensional marginals for both distributions are presented.

A fractional generalization of the Dirichlet distribution and related distributions

Elvira Di Nardo;Federico Polito;
2021

Abstract

This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the n partitions of the interval [0, Wn] are independent and identically distributed random variables following the generalized Mittag-Leffler distribution. The expected value and variance of the one-dimensional marginal are derived as well as the form of its probability density function. A related generalized Dirichlet distribution is studied that provides a reasonable approximation for some values of the parameters. The relation between this distribution and other generalizations of the Dirichlet distribution is discussed. Monte Carlo simulations of the one-dimensional marginals for both distributions are presented.
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https://arxiv.org/pdf/2101.04481.pdf
Fractional Dirichlet distribution, Generalized Dirichlet distribution, Three-parameter Mittag-Leffler functions, Fractional Poisson process, Wealth distribution, Power-law tails.
Elvira Di Nardo, Federico Polito, Enrico Scalas
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/1766846
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