New classes of random discrete distributions on infinite simplex and their stick-breaking properties

Event status:

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.

Date:
Friday 26 May 2017 12:00 pm until Friday 26 May 2017 01:00 pm (Add to calendar)
Contact:
Andriy Olenko
0394792609; A.Olenko@latrobe.edu.au
Presented by:
Dr Yuguang Fan (Australian National University)
Type of Event:
Public Lecture

(A joint work with Prof. Ross Maller)

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.

Map:

Room 310 (ACE Room), Physical Sciences 2

La Trobe University

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