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A fractional generalization of the Dirichlet distribution and related distributions

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journal contribution
posted on 2023-06-09, 22:46 authored by Elvira Di Nardo, Federico Polito, Enrico Scalas
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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Fractional Calculus and Applied Analysis

ISSN

1311-0454

Publisher

De Gruyter

Issue

1

Volume

24

Page range

112-136

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Notes

ArXiv link: https://arxiv.org/abs/2101.04481

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2021-01-15

First Open Access (FOA) Date

2022-01-30

First Compliant Deposit (FCD) Date

2021-01-14

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