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SUMMARY:A fractional generalisation of the Dirichlet distribution - Enrico
   Scalas (University of Sussex)
DTSTART:20220328T161500Z
DTEND:20220328T171500Z
UID:TALK170057@talks.cam.ac.uk
DESCRIPTION:A generalisation of the Dirichlet distribution is derived assu
 ming that the $n$ partitions of the interval $[0\, W_n]$ are independent a
 nd identically distributed random variables following the generalized Mitt
 ag-Leffler distribution. The expected value and variance of the one-dimens
 ional marginal are presented as well as the form of its probability densit
 y function. A related generalized Dirichlet distribution is studied that p
 rovides a reasonable approximation for some values of the parameters. The 
 relation between this distribution and other generalizations of the Dirich
 let distribution is discussed. Monte Carlo simulations of the one-dimensio
 nal marginals for both distributions are presented.\nThe results of this t
 alk were presented in a paper in collaboration with Elvira Di Nardo and Fe
 derico Polito:\nElvira Di Nardo\, Federico Polito\, Enrico Scalas\nA fract
 ional generalisation of the Dirichlet distribution and related distributio
 ns\nFract. Calc. Appl. Anal.\, Vol. 24\, No 1 (2021)\, pp. 112&ndash\;136\
 ,DOI: 10.1515/fca-2021-0006\nThese results are part of a wider research pr
 ogram on random exchange processes for the distribution of wealth. This re
 search program will be briefly introduced in my talk.
LOCATION:Seminar Room 2\, Newton Institute
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