Journal
ADVANCES IN APPLIED PROBABILITY
Volume 42, Issue 2, Pages 433-459Publisher
APPLIED PROBABILITY TRUST
DOI: 10.1239/aap/1275055237
Keywords
Conditional identity in distribution; Poisson-Dirichlet sequence; random partition; random probability measure; randomly reinforced urn; species sampling sequence; stable convergence
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Funding
- GNAMPA [2009]
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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.
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