Ebook: The Conway–Maxwell–Poisson Distribution
Author: Kimberly F. Sellers
- Genre: Mathematics // Probability
- Tags: Conway, Maxwell, Poisson, Conway Maxwell Poisson, Conway–Maxwell–Poisson, Distribution, Probability Theory, Statistics, Statistics Theory, Statistics Methods, Economics, Econometrics, Mathematical Methods, R Programming Language
- Series: Institute of Mathematical Statistics Monographs 8
- Year: 2023
- Publisher: Cambridge University Press
- City: Cambridge
- Edition: 1
- Language: English
- pdf
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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