In probability theory, a Pitman–Yor process[1] [2] ,[3] denoted PY(d, θ, G0), is a stochastic process whose sample path is a probability distribution. A random sample from this process is a finite-dimensional Pitman–Yor distribution, named after Jim Pitman and Marc Yor. Unfortunately, there is no known analytic form for this distribution.
The parameters governing the Pitman–Yor process are: 0 ≤ d ≤ 1 a discount parameter, a strength parameter θ > −d and a base distribution G0 over a probability space X. When d = 0, it becomes the Dirichlet process. The discount parameter gives the Pitman–Yor process more flexibility over tail behavior than the Dirichlet process, which has exponential tails. This makes Pitman–Yor process useful for modeling data with power-law tails (e.g., word frequencies in natural language).