English

A fractional generalization of the Dirichlet distribution and related distributions

Probability 2021-02-17 v1

Abstract

This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the nn partitions of the interval [0,Wn][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.

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}
}