Poisson-Dirichlet Distribution

The Poisson-Dirichlet distribution with parameter is the statistical distribution of the decreasing rearrangement of the fragments of a random stick-breaking construction. In this one-parameter convention, also denoted , take independent random variables with probability density function on and put

The decreasing rearrangement has nonnegative entries summing to 1 almost surely. For , the variables have a uniform distribution on .

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References

Pitman, J. and Yor, M. "The Two-Parameter Poisson-Dirichlet Distribution Derived from a Stable Subordinator." Ann. Probab. 25, 855-900, 1997. https://doi.org/10.1214/aop/1024404422.

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Weisstein, Eric W. "Poisson-Dirichlet Distribution." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Poisson-DirichletDistribution.html

Poisson-Dirichlet Distribution

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