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.