Starting with a stable subordinator, the sequence of ordered jumps up till time 1, omitting the r largest of them, and taken as proportions of their sum defines a 2-parameter distribution on the infinite dimensional simplex. When r = 0, it reduces to Poisson-Dirichlet distribution introduced by Kingman in 1975. We observe a serendipitous connection between the new class of distributions and the negative binomial point process of Gregoire (1984), which we exploit to analyse in detail a corresponding size-biased version of the new class of distributions.  As a consequence we derive a stick-breaking representation for the process and a useful form for its distribution. This program produces a large new class of distributions available for a variety of modelling purposes.

This is joint work with Prof. Ross Maller.


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