A random sample from this process is an infinite discrete probability distribution, consisting of an infinite set of atoms drawn from G0, with weights drawn from a two-parameter Poisson-Dirichlet distribution.
The process is named after Jim Pitman and Marc Yor.
This makes Pitman–Yor process useful for modeling data with power-law tails (e.g., word frequencies in natural language).
The name "Pitman–Yor process" was coined by Ishwaran and James[5] after Pitman and Yor's review on the subject.
[2] However the process was originally studied in Perman et al.[6][7] It is also sometimes referred to as the two-parameter Poisson–Dirichlet process, after the two-parameter generalization of the Poisson–Dirichlet distribution which describes the joint distribution of the sizes of the atoms in the random measure, sorted by strictly decreasing order.