A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution

By Galit Shmueli, Tom Minka, J. Kadane, Sharad Borle, Peter Boatwright. 2005

633 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/52b7a2f7c264ea2898021d5f4a858b29726989d5

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Citations in the corpus

Underdispersion models: Models that are “under the radar” (2017, background): “Shmueli et al. (2005) provides the following recursive relationship for the moments: E(Yr+1) = { λ[E(Y + 1)]1−ν r = 0 λ ∂ ∂λ E(Yr) + E(Y )E(Yr) r > 0, (8) where E(Yr) = ∑∞y=0 yrP(Y = y) denotes the rth moment of a random variable Y with pmf P(Y = y) as defined in Equation (5).”
A Flexible Regression Model for Count Data (2010, positive): “A two-parameter generalized form of the Poisson distribution, called the Conway–Maxwell-Poisson (COM-Poisson) distribution [Shmueli et al. (2005)], is sufficiently flexible to describe a wide range of count data distributions.”
Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics (2017, background): “(100) is that of a ConwayMaxwell-Poisson distribution [120, 9].”
Mean-parametrized Conway–Maxwell–Poisson regression models for dispersed counts (2016, methodology): “In contrast, estimation of the rate parameter λ in the standard CMP model is far more complicated, with Shmueli et al. (2005) giving three alternative estimation schemes for λ for the iid case alone.”
glmmTMB Balances Speed and Flexibility Among Packages for Zero-inflated Generalized Linear Mixed Modeling (2017, methodology): “When data are either over-or underdispersed, they can be modeled with the lesser-known, Conway-Maxwell-Poisson distribution (Shmueli et al., 2005; Lynch et al., 2014; Barriga and Louzada, 2014).”