Answer by Clarinetist for Is the canonical parameter (and therefore the...
The systematic component of the GLM is $$g(\mu_i) = \mathbf{x}_i^{\prime}\boldsymbol\beta\text{.}$$As long as we do not place any restrictions on the $\boldsymbol\beta$ coefficients, without loss of...
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Consider $Y_1, \dots, Y_n$ independent from the Gamma distribution. For $y > 0$:$$\begin{align}f(y \mid \alpha, \beta) &= \dfrac{1}{\beta^{\alpha}\Gamma(\alpha)}y^{\alpha-1}e^{-y/\beta} \\&=...
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