The Conway–Maxwell–Poisson Distribution

Kimberly F. Sellers

mar 2023 · Institute of Mathematical Statistics Monographs Libro 8 · Cambridge University Press

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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.

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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.