  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 $[0,W_n]$ 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.
