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A fractional generalisation of the Dirichlet distribution

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FDE2 - Fractional differential equations

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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