Displaced Poisson distribution
In statistics, the displaced Poisson, also known as the hyper-Poisson distribution, is a generalization of the Poisson distribution.
The probability mass function is
where and r is a new parameter; the Poisson distribution is recovered at r = 0. Here is the Pearson's incomplete gamma function:
where s is the integral part of r.
The motivation given by Staff is that the ratio of successive probabilities in the Poisson distribution is given by for and the displaced Poisson generalizes this ratio to.
