The Conway–Maxwell–Poisson Distribution

Kimberly F. Sellers

doi:10.1017/9781108646437

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.

‘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

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The Conway–Maxwell–Poisson Distribution

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Contents

Frontmatter
pp i-iv

Dedication
pp v-vi

Contents
pp vii-xi

Figures
pp xii-xiii

Tables
pp xiv-xx

Preface
pp xxi-xxii

Acknowledgments
pp xxiii-xxiv

1 - Introduction: Count Data Containing Dispersion
pp 1-21

2 - The Conway–Maxwell–Poisson (COM–Poisson) Distribution
pp 22-70

3 - Distributional Extensions and Generalities
pp 71-123

4 - Multivariate Forms of the COM–Poisson Distribution
pp 124-152

5 - COM–Poisson Regression
pp 153-217

6 - COM–Poisson Control Charts
pp 218-250

7 - COM–Poisson Models for Serially Dependent Count Data
pp 251-283

8 - COM–Poisson Cure Rate Models
pp 284-311

References
pp 312-326

Index
pp 327-330

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