Poisson-Dirichlet distribution arises in many different areas. The parameter θ in the distribution is the scaled mutation rate of a population in the context of population genetics. The limiting procedure of θ approaching infinity is practically motivated and has led to new interesting mathematical structures. Results of law of large numbers, fluctuation theorems and large deviations have been ...

The compound Poisson-gamma variable is the sum of a random sample from a gamma distribution with sample size an independent Poisson random variable. It has received wide ranging applications. In this note, we give an account of its mathematical properties including estimation procedures by the methods of moments and maximum likelihood. Most of the properties given are hitherto unknown.

A branching process is a mathematical description of the growth of a population for which the individual produces offsprings according to stochastic laws. A typical problem would be of the following form. Considering a population of individuals developing from a single progenitor, the initial individual. The initial individual produces a random number of offsprings, each of them in turn produce...

This paper presents a method for the evaluation of the compound Generalized Poisson distribution, based on the recursive evaluation of two other distributions.