A fractional generalization of the Dirichlet distribution and related distributions

Di Nardo, Elvira, Polito, Federico and Scalas, Enrico (2021) A fractional generalization of the Dirichlet distribution and related distributions. Fractional Calculus and Applied Analysis, 24 (1). pp. 112-136. ISSN 1311-0454

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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, 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.

Item Type: Article
Additional Information: ArXiv link: https://arxiv.org/abs/2101.04481
Keywords: Fractional Dirichlet distribution, Generalized Dirichlet distribution, Three-parameter Mittag-Leffler functions, Fractional Poisson process, Wealth distribution, Power-law tails
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Probability and Statistics Research Group
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 15 Jan 2021 09:03
Last Modified: 02 Mar 2021 11:00
URI: http://sro.sussex.ac.uk/id/eprint/96507

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