Definitions
Tweedie distributions are a special case of exponential dispersion models, a class of models used to describe error distributions for the generalized linear model. The term exponential dispersion model refers to the exponential form that these models take, evident from the canonical equation used to describe the distribution Pλ,θ of the random variable Z on the measurable sets A,
- ,
with the interrelated measures νλ. θ is the canonical parameter; the cumulant function is
- ;
λ is the index parameter; and z the canonical statistic. This equation represents a family of exponential dispersion models ED*(θ,λ) that are completely determined by the parameters θ and λ and the cumulant function.
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