# The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator

@article{Pitman1997TheTP, title={The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator}, author={Jim Pitman and Marc Yor}, journal={Annals of Probability}, year={1997}, volume={25}, pages={855-900} }

The two-parameter Poisson-Dirichlet distribution, denoted PD(α,θ), is a probability distribution on the set of decreasing positive sequences with sum 1. The usual Poisson-Dirichlet distribution with a single parameter θ, introduced by Kingman, is PD(0, θ). Known properties of PD(0, θ), including the Markov chain description due to Vershik, Shmidt and Ignatov, are generalized to the two-parameter case. The size-biased random permutation of PD(α, θ) is a simple residual allocation model proposed…

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