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A Simple and Adaptive Dispersion Regression Model for Count Data

Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Department of Mathematics, Brunel University London, Uxbridge UB8 3PH, UK
Author to whom correspondence should be addressed.
Entropy 2018, 20(2), 142;
Received: 19 January 2018 / Revised: 14 February 2018 / Accepted: 16 February 2018 / Published: 22 February 2018
(This article belongs to the Special Issue Power Law Behaviour in Complex Systems)
PDF [409 KB, uploaded 22 February 2018]


Regression for count data is widely performed by models such as Poisson, negative binomial (NB) and zero-inflated regression. A challenge often faced by practitioners is the selection of the right model to take into account dispersion, which typically occurs in count datasets. It is highly desirable to have a unified model that can automatically adapt to the underlying dispersion and that can be easily implemented in practice. In this paper, a discrete Weibull regression model is shown to be able to adapt in a simple way to different types of dispersions relative to Poisson regression: overdispersion, underdispersion and covariate-specific dispersion. Maximum likelihood can be used for efficient parameter estimation. The description of the model, parameter inference and model diagnostics is accompanied by simulated and real data analyses. View Full-Text
Keywords: discrete Weibull; count data; dispersion; generalised linear models discrete Weibull; count data; dispersion; generalised linear models

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Klakattawi, H.S.; Vinciotti, V.; Yu, K. A Simple and Adaptive Dispersion Regression Model for Count Data. Entropy 2018, 20, 142.

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