Cumulative distribution function of a geometric Poisson distribution

Abstract

The geometric Poisson distribution (also called Pólya–Aeppli) is a particular case of the compound Poisson distribution. We propose to express the general term of this distribution through a recurrence formula leading to a linear algorithm for the computation of its cumulative distribution function. Practical implementation with a special care for numerical computations is proposed and validated. The article ends with an example of application of these results for the computation of pattern statistics in biological sequences modelized by a Markov model.

Keywords:

• Compound Poisson
• Pólya–Aeppli
• Confluent hypergeometric function
• Kummer

Additional information

Notes on contributors

Grégory Nuel

Email: [email protected]