On the distribution of points in a Poisson Dirichlet process

A probability density function important in the Poisson Dirichlet process of population genetics is studied. An accurate computational algorithm is given for this density and for the marginal distributions of the points in the Poisson Dirichlet process. The distribution of the maximal point of the process is tabulated. Rational polynomial approximations in θ, the mutation parameter, are found for the expected values of the first three maximal points.