The Conway–Maxwell–Poisson Distribution

The first coherent introduction to the Conway-Maxwell-Poisson distribution and its contributions in statistical theory and computing in R.

Kimberly F. Sellers (Author)

9781108481106, Cambridge University Press

Hardback, published 9 March 2023

250 pages
23.5 x 15.5 x 2.5 cm, 0.65 kg

'This book is a terrific one-stop-shop for 'everything COM-Poisson', not only integrating theoretical knowledge around the Conway-Maxwell Poisson distribution and its uses, but also providing practical notes and tips for applying the various relevant R libraries. Researchers and practitioners modeling count data or developing tools for modeling count data should find this book highly useful.' Galit Shmueli, National Tsing Hua University

While the Poisson distribution is a classical statistical model for count data, the distributional model hinges on the constraining property that its mean equal its variance. This text instead introduces the Conway-Maxwell-Poisson distribution and motivates its use in developing flexible statistical methods based on its distributional form. This two-parameter model not only contains the Poisson distribution as a special case but, in its ability to account for data over- or under-dispersion, encompasses both the geometric and Bernoulli distributions. The resulting statistical methods serve in a multitude of ways, from an exploratory data analysis tool, to a flexible modeling impetus for varied statistical methods involving count data. The first comprehensive reference on the subject, this text contains numerous illustrative examples demonstrating R code and output. It is essential reading for academics in statistics and data science, as well as quantitative researchers and data analysts in economics, biostatistics and other applied disciplines.

Preface
1. Introduction: count data containing dispersion
2. The Conway-Maxwell-Poisson (COM-Poisson) distribution
3. Distributional extensions and generalities
4. Multivariate forms of the COM-Poisson distribution
5. COM-Poisson regression
6. COM-Poisson control charts
7. COM-Poisson models for serially dependent count data
8. COM-Poisson cure rate models
Bibliography
Index.

Subject Areas: Probability & statistics [PBT], Mathematics [PB], Mathematics & science [P], Epidemiology & medical statistics [MBNS]