for some functions a_{i}(Φ) = Φ/wi, b and c_{i} = c(y_{i}, Φ/wi), where wi is a known weight for each observation. Hereby, θ_{i} 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, w_{i} = 1 for all i) and then the scaling simpli?es to a_{i}(Φ) = Φ), whereas c_{i}(y_{i}, Φ) becomes just c(y_{i}, Φ) and (1) simpli?es to
It can be shown from a standard theory for these distributions that