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Record indices and age-ordered frequencies in exchangeable Gibbs partitions

Abstract:

The frequencies X1, X2, . . . of an exchangeable Gibbs random partition Π of ℕ -{1,2, . . . } (Gnedin and Pitman (2005)) are considered in their age-order, i.e. their size-biased order. We study their dependence on the sequence i1, i2, . . . of least elements of the blocks of Π. In particular, conditioning on 1 = i1 < i2 < . . ., a representation is shown to be Xj = ξj-1 Πi=j∞(1 - ξi) j = 1, 2, . . . where {ξj = 1, 2, . . . } is a sequence of independent Beta random variables. Sequences...

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Publication status:
Published

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Institution:
University of Oxford
Department:
Oxford, MPLS, Statistics
Role:
Author
Journal:
ELECTRONIC JOURNAL OF PROBABILITY
Volume:
12
Pages:
1101-1130
Publication date:
2007-08-25
EISSN:
1083-6489
ISSN:
1083-6489
URN:
uuid:6d3e38eb-ea0f-48e9-90a6-171e12d66e9e
Source identifiers:
97760
Local pid:
pubs:97760

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