A fractional generalization of the Dirichlet distribution and related distributions

Elvira Di Nardo; Federico Polito; Enrico Scalas

doi:10.1515/fca-2021-0006

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arXiv · 2101.04481

A fractional generalization of the Dirichlet distribution and related distributions

Elvira Di Nardo·Federico Polito·Enrico Scalas

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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 $[0,W_n]$ 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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Elvira Di Nardo, Federico Polito, Enrico Scalas. 2021-01-12. A fractional generalization of the Dirichlet distribution and related distributions. https://doi.org/10.1515/fca-2021-0006

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