The Conway–Maxwell–Poisson Distribution
Seiten
2023
Cambridge University Press (Verlag)
978-1-108-48110-6 (ISBN)
Cambridge University Press (Verlag)
978-1-108-48110-6 (ISBN)
This is the first comprehensive introduction to the Conway-Maxwell-Poisson distribution and its contributions in statistical theory and computing in R, including its uses in count data modelling. An essential reference for academics in statistics and data science, as well as quantitative researchers and data analysts in applied disciplines.
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.
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.
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.
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.
| Erscheinungsdatum | 27.02.2023 |
|---|---|
| Reihe/Serie | Institute of Mathematical Statistics Monographs |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 650 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| Studium ► Querschnittsbereiche ► Epidemiologie / Med. Biometrie | |
| Naturwissenschaften | |
| ISBN-10 | 1-108-48110-8 / 1108481108 |
| ISBN-13 | 978-1-108-48110-6 / 9781108481106 |
| Zustand | Neuware |
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