Abstract

A generalisation of the Dirichlet 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 presented 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. The results of this talk were presented in a paper in collaboration with Elvira Di Nardo and Federico Polito: Elvira Di Nardo, Federico Polito, Enrico Scalas A fractional generalisation of the Dirichlet distribution and related distributions Fract. Calc. Appl. Anal., Vol. 24, No 1 (2021), pp. 112–136,DOI: 10.1515/fca-2021-0006 These results are part of a wider research program on random exchange processes for the distribution of wealth. This research program will be briefly introduced in my talk.