2017
DOI: 10.1177/1471082x17715718
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Extended Poisson–Tweedie: Properties and regression models for count data

Abstract: We propose a new class of discrete generalized linear models based on the class of Poisson-Tweedie factorial dispersion models with variance of the form µ + φµ p , where µ is the mean, φ and p are the dispersion and Tweedie power parameters, respectively. The models are fitted by using an estimating function approach obtained by combining the quasi-score and Pearson estimating functions for estimation of the regression and dispersion parameters, respectively. This provides a flexible and efficient regression m… Show more

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Cited by 76 publications
(56 citation statements)
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“…This package fits a Tweedie compound Poisson distribution for the response (log link), which is ideal for data that contains measured zeros as well as a continuous positive distribution of densities (Bonat et al. ). Coefficients are estimated using maximum likelihood based on the LaPlace approximation (Zhang ).…”
Section: Methodsmentioning
confidence: 99%
“…This package fits a Tweedie compound Poisson distribution for the response (log link), which is ideal for data that contains measured zeros as well as a continuous positive distribution of densities (Bonat et al. ). Coefficients are estimated using maximum likelihood based on the LaPlace approximation (Zhang ).…”
Section: Methodsmentioning
confidence: 99%
“…'s) which are hereinafter referred to as the Poisson-Tweedie mixtures. This family was considered, among many others, by Kokonendji et al (2004, Section 3), Jørgensen and Kokonendji (2016), and Bonat et al (2017). The Poisson-Tweedie mixtures are rigorously introduced by formula (3).…”
Section: Introductionmentioning
confidence: 99%
“…Para uma variável aleatória Z com distribuição Tweedie, escrevemos µ e Var(Y ) = µ + ϕµ p . Esse fato motiva a especificação de um modelo baseado apenas em suposições de momentos de segunda-ordem (Bonat et al, 2018). Sendo assim, a função de variância para esta família de distribuições é ϑ(µ; p) = µ + ϕµ p , em que modelos importantes para dados de contagem são casos particulares, como Hermite (p = 0),…”
Section: Modelosunclassified
“…As estimativas dos parâmetros de regressão são realizadas pelo método de quaseescore, e os parâmetros de dispersão pelas funções de estimação de Pearson. A formulação do modelo Poisson-Tweedie é exatamente a mesma daquela para os modelos quase-binomial e quase-Poisson no contexto de GLMs (Bonat et al, 2018). 4.3.…”
Section: Modelosunclassified