Stick-breaking PG(\alpha,\zeta)-Generalized Gamma Processes

Understand

This work centers around results related to Proposition 21 of Pitman and Yor's (1997) paper on the two parameter Poisson Dirichlet distribution indexed by (\alpha,\theta) for 0<\alpha<1, also \alpha=0, and \theta>-\alpha, denoted PD(\alpha,\theta).

• We develop explicit stick-breaking representations for a class that contains the PD(\alpha,\theta) for the range \theta=0, and \theta>0, we call PG(\alpha,\zeta).
• We also construct a larger class, EPG(\alpha,\zeta), containing the entire range.
• These classes are indexed by \alpha, and an arbitrary non-negative random variable \zeta.