The Touchard distribution

ABSTRACT

We present a novel model, which is a two-parameter extension of the Poisson distribution. Its normalizing constant is related to the Touchard polynomials, hence the name of this model. It is a flexible distribution that can account for both under- or overdispersion and concentration of zeros that are frequently found in non-Poisson count data. In contrast to some other generalizations, the Hessian matrix for maximum likelihood estimation of the Touchard parameters has a simple form. We exemplify with three data sets, showing that our suggested model is a competitive candidate for fitting non-Poisson counts.

KEYWORDS:

• Generalized power series distribution
• Overdispersion
• Poisson distribution
• Touchard distribution
• Underdispersion
• Zero-inflated distribution.

MATHEMATICS SUBJECT CLASSIFCATION:

• Primary 62E15
• Secondary 60E15

Additional information

Funding

This work was partially supported by FAPDF. We also thank the referees whose comments helped to improve our paper.