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for some functions ai(Φ) = Φ/wi, b and ci = c(yi, Φ/wi), where wi is a known weight for each observation. Hereby, θi is called canonical parameter whereas Φ is called the dispersion parameter.
Note: For most models, the weight is the same for each i (that is, wi = 1 for all i) and then the scaling simpli?es to ai(Φ) = Φ), whereas ci(yi, Φ) becomes just c(yi, Φ) and (1) simpli?es to
It can be shown from a standard theory for these distributions that
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