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Conditionally identically distributed species sampling sequences

Part of: Stochastic processes Probability theory on algebraic and topological structures Limit theorems

Published online by Cambridge University Press:  01 July 2016

Federico Bassetti ,
Irene Crimaldi  and
Fabrizio Leisen
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.

Keywords

Conditional identity in distributionPoisson-Dirichlet sequencerandom partitionrandom probability measurerandomly reinforced urnspecies sampling sequencestable convergence

MSC classification

Primary: 60F05: Central limit and other weak theorems 60G57: Random measures 60B10: Convergence of probability measures
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 42 , Issue 2 , June 2010 , pp. 433 - 459
Copyright
Copyright © Applied Probability Trust 2010 

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