New Class of Random Discrete Distributions on Infinite Simplex Derived from Negative Binomial Processes

Friday October 19, 2pm, Carslaw 173

Yuguang Ipsen
Australian National University, Research School of Finance, Actuarial Studies & Statistics

New Class of Random Discrete Distributions on Infinite Simplex Derived from Negative Binomial Processes

The Poisson-Kingman distributions, PK(ρ), on the infinite simplex, can be constructed from a Poisson point process having intensity density ρ or by taking the ranked jumps up till a specified time of a subordinator with Levy density ρ, as proportions of the subordinator. As a natural extension, we replace the Poisson point process with a negative binomial point process having parameter r > 0 and Levy density ρ, thereby defining a new class PK^{(r)}(ρ) of distributions on the infinite simplex. The new class contains the two-parameter generalisation PD(α,θ) of Pitman and Yor (1997) when θ > 0. It also contains a class of distributions, PD_α(r) occurs naturally from the trimmed stable subordinator. We derive properties of the new distributions, including the joint density of its size-biased permutation, a stick-breaking representation as well as the exchangeable partition probability function and an analogous Ewens sampling formula for PD_α(r).

Joint work with Prof. Ross Maller and Dr. Soudabeh Shemehsavar.