Author ORCID Identifier
Document Type
Article
Publication Date
2017
Publication Title
Journal of Statistical Distributions and Applications
Volume
4
Issue
22
Abstract
The Poisson, geometric and Bernoulli distributions are special cases of a flexible count distribution, namely the Conway-Maxwell-Poisson (CMP) distribution – a two-parameter generalization of the Poisson distribution that can accommodate data over- or under-dispersion. This work further generalizes the ideas of the CMP distribution by considering sums of CMP random variables to establish a flexible class of distributions that encompasses the Poisson, negative binomial, and binomial distributions as special cases. This sum-of-Conway-Maxwell-Poissons (sCMP) class captures the CMP and its special cases, as well as the classical negative binomial and binomial distributions. Through simulated and real data examples, we demonstrate this model’s flexibility, encompassing several classical distributions as well as other count data distributions containing significant data dispersion.
Recommended Citation
Sellers, Kimberly F.; Swift, Andrew W.; and Weems, Kimberly S., "A flexible distribution class for count data" (2017). Mathematics Faculty Publications. 66.
https://digitalcommons.unomaha.edu/mathfacpub/66
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Comments
© The Author(s). 2017
https://link.springer.com/article/10.1186/s40488-017-0077-0
DOI 10.1186/s40488-017-0077-0