Theoretical and Applied Statistics by Corrado Crocetta

Author:Corrado Crocetta
Language: eng
Format: epub
ISBN: 9783030054205
Publisher: Springer International Publishing

(9)

This formula is well-known to correspond to the EPPF induced by the Poisson-Dirichlet random discrete distribution, the law of the ranked random atoms of the Dirichlet process [11, 19], hence to be a particular case of (4) for and . It follows that specializing (5) and (6), expected first and second moment of Gini-Simpson’s index under Ewens neutral model are given by

(10)

and

(11)

Additionally, from (7) and (8), conditional first and second moments of are as follows:

(12)

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