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Lookup NU author(s): Dr Vianey Palacios RamirezORCiD
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While random probability measures have a long tradition in probability and statis-tics, little is known about their tails. The few available results are derived using subordinators,and therefore only apply to measures that can be represented as normalized subordinators, suchas the Dirichlet process. Our work breaks this barrier, by exploiting the stick-breaking represen-tation to construct a new family of transport maps that preserve the decay of tails. Drawing onrecent developments on regular variation and on subordinator theory, the new family of mapsallows us to establish that the right tail of a Pitman–Yor process is heavy-tailed if the centeringdistribution is itself heavy-tailed; the Dirichlet process is the only member of this class thatfails to obey this convenient property. Asymptotic envelopes for the tails of the Pitman–Yorprocesses are also derived. Finally, we discuss some consequences of the main results, includingaspects related to the posterior distribution.
Author(s): Gil Leyva M, Palacios Ramirez V, de Carvalho M
Publication type: Article
Publication status: In Press
Journal: Extremes
Year: 2026
Acceptance date: 02/02/2026
ISSN (print): 1386-1999
ISSN (electronic): 1572-915X
Publisher: Springer New York LLC
