The Conway–Maxwell–Poisson Distribution

Kimberly F. Sellers (Georgetown University, Washington DC)

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English

Cambridge University Press
10 July 2025

Epidemiology & medical statistics; Probability & statistics

Series: Institute of Mathematical Statistics Monographs

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.

By: Kimberly F. Sellers (Georgetown University Washington DC)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
ISBN: 9781009667135
ISBN 10: 1009667130
Series: Institute of Mathematical Statistics Monographs
Pages: 354
Publication Date: 10 July 2025
Audience: College/higher education , Further / Higher Education
Format: Paperback
Publisher's Status: Active

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.

Kimberly F. Sellers is Professor in the Department of Mathematics and Statistics at Georgetown University, and a Principal Researcher with the Center for Statistical Research and Methodology at the US Census Bureau in Washington, DC. She is a Fellow of the American Statistical Association and an Elected Member of the International Statistical Institute.

Reviews for The Conway–Maxwell–Poisson Distribution

'This book will be a great resource for anyone interested in modeling or analyzing count data. It offers a comprehensive perspective on the Conway-Maxwell-Poisson distribution.' Somnath Datta, University of Florida '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