The Conway-Maxwell-Poisson Distribution

Erscheinungsjahr 2023
ISBN: 978-1-108-48110-6
Verlag: Cambridge University Press

Buch, Englisch, Band 8, 250 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 689 g

Reihe: 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.

Autoren/Hrsg.

Sellers, Kimberly F

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

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.

Über Autor(innen)

Sellers, Kimberly F
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.