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Conditionally identically distributed species sampling sequences

Published online by Cambridge University Press:  01 July 2016

Federico Bassetti*
Affiliation:
University of Pavia
Irene Crimaldi*
Affiliation:
University of Bologna
Fabrizio Leisen*
Affiliation:
University of Navarra
*
Postal address: Department of Mathematics, University of Pavia, via Ferrata 1, 27100 Pavia, Italy. Email address: federico.bassetti@unipv.it
∗∗ Postal address: Department of Mathematics, University of Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy. Email address: crimaldi@dm.unibo.it
∗∗∗ Postal address: Faculty of Economics, University of Navarra, Campus Universitario, Edificio de Biblioteca (Entrada Este), 31008, Pamplona, Spain. Email address: fabrizio.leisen@unimore.it
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Abstract

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In this paper the theory of species sampling sequences is linked to the theory of conditionally identically distributed sequences in order to enlarge the set of species sampling sequences which are mathematically tractable. The conditional identity in distribution (see Berti, Pratelli and Rigo (2004)) is a new type of dependence for random variables, which generalizes the well-known notion of exchangeability. In this paper a class of random sequences, called generalized species sampling sequences, is defined and a condition to have conditional identity in distribution is given. Moreover, two types of generalized species sampling sequence that are conditionally identically distributed are introduced and studied: the generalized Poisson-Dirichlet sequence and the generalized Ottawa sequence. Some examples are discussed.

Type
General Applied Probability
Copyright
Copyright © Applied Probability Trust 2010 

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