Discrete dispersion models and their Tweedie asymptotics
نویسندگان
چکیده
منابع مشابه
evaluation of Tweedie exponential dispersion model densities ∗
Exponential dispersion models, which are linear exponential families with a dispersion parameter, are the prototype response distributions for generalized linear models. The Tweedie families are those exponential dispersion models with power mean-variance relationships. The normal, Poisson, gamma and inverse Gaussian distributions are Tweedie families. Apart from these special cases, Tweedie di...
متن کاملSeries evaluation of Tweedie exponential dispersion model densities
Exponential dispersion models, which are linear exponential families with a dispersion parameter, are the prototype response distributions for generalized linear models. The Tweedie families are those exponential dispersion models with power mean-variance relationships. The normal, Poisson, gamma and inverse Gaussian distributions are Tweedie families. Apart from these special cases, Tweedie di...
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The Tweedie family of distributions is a family of exponential dispersion models with power variance functions V (μ) = μp for p 6∈ (0, 1). These distributions do not generally have density functions that can be written in closed form. However, they have simple moment generating functions, so the densities can be evaluated numerically by Fourier inversion of the characteristic functions. This pa...
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We describe the underlying probabilistic interpretation of alpha and beta divergences. We first show that beta divergences are inherently tied to Tweedie distributions, a particular type of exponential family, known as exponential dispersion models. Starting from the variance function of a Tweedie model, we outline how to get alpha and beta divergences as special cases of Csiszár’s f and Bregma...
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R2-type measures are commonly used tools for assessing the predictive power of linear regression models; for generalized linear models this measure is based on deviances. For small samples, it is necessary to adjust R2 for the number of covariates. This article shows that some of the adjustments that have been proposed for logistic, Poisson, gamma and inverse Gaussian models, can be expressed i...
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ژورنال
عنوان ژورنال: AStA Advances in Statistical Analysis
سال: 2015
ISSN: 1863-8171,1863-818X
DOI: 10.1007/s10182-015-0250-z