A fractional generalization of the Dirichlet distribution and related distributions
Abstract
This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the partitions of the interval 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.
Keywords
Cite
@article{arxiv.2101.04481,
title = {A fractional generalization of the Dirichlet distribution and related distributions},
author = {Elvira Di Nardo and Federico Polito and Enrico Scalas},
journal= {arXiv preprint arXiv:2101.04481},
year = {2021}
}