\[\mathbf{Var}\left( \mathbf{Y} \right)\]	Related Distribution	Estimating Equations (Log-Link)
\[\phi\]	Normal	\[\sum_{}^{}{{y_{i} \cdot w}_{i} \cdot \left( \mu_{i} \right) \cdot x_{i,j}} = \ \sum_{}^{}{{\mu_{i} \cdot w}_{i} \cdot \left( \mu_{i} \right) \cdot x_{i,j}}\]
\[\phi \cdot \mu\]	Poisson	\[\sum_{}^{}{{y_{i} \cdot w}_{i} \cdot x_{i,j}} = \ \sum_{}^{}{{\mu_{i} \cdot w}_{i} \cdot x_{i,j}}\]
\[\phi \cdot \mu^{2}\]	Gamma	\[\sum_{}^{}{{y_{i} \cdot w}_{i} \cdot \left( \mu_{i}^{- 1} \right) \cdot x_{i,j}} = \ \sum_{}^{}{{\mu_{i} \cdot w}_{i} \cdot \left( \mu_{i}^{- 1} \right) \cdot x_{i,j}}\]
\[\phi \cdot \mu^{3}\]	Inverse Gaussian	\[\sum_{}^{}{{y_{i} \cdot w}_{i} \cdot \left( \mu_{i}^{- 2} \right) \cdot x_{i,j}} = \ \sum_{}^{}{{\mu_{i} \cdot w}_{i} \cdot \left( \mu_{i}^{- 2} \right) \cdot x_{i,j}}\]
\[\phi \cdot \mu^{p}\]	Tweedie	\[\sum_{}^{}{{y_{i} \cdot w}_{i} \cdot \left( \mu_{i}^{1 - p} \right) \cdot x_{i,j}} = \ \sum_{}^{}{{\mu_{i} \cdot w}_{i} \cdot \left( \mu_{i}^{1 - p} \right) \cdot x_{i,j}}\]
\[\phi \cdot \left( \mu + \frac{1}{k} \cdot \mu^{2} \right)\]	Negative Binomial	\[\sum_{}^{}{{y_{i} \cdot w}_{i} \cdot \left( \frac{k}{k + \mu_{i}} \right) \cdot x_{i,j}} = \ \sum_{}^{}{{\mu_{i} \cdot w}_{i} \cdot \left( \frac{k}{k + \mu_{i}} \right) \cdot x_{i,j}}\]
\[\phi \cdot \left( \mu + \frac{1}{k} \cdot \mu^{3} \right)\]	Poisson-Inverse Gaussian	\[\sum_{}^{}{{y_{i} \cdot w}_{i} \cdot \left( \frac{k}{k + \mu_{i}^{2}} \right) \cdot x_{i,j}} = \ \sum_{}^{}{{\mu_{i} \cdot w}_{i} \cdot \left( \frac{k}{k + \mu_{i}^{2}} \right) \cdot x_{i,j}}\]
\[\phi \cdot exp\left( \frac{1}{k} \cdot \mu \right)\]	???	\[\sum_{}^{}{{y_{i} \cdot w}_{i} \cdot \left( \mu_{i} \cdot e^{- \mu_{i}/k} \right) \cdot x_{i,j}} = \ \sum_{}^{}{{\mu_{i} \cdot w}_{i} \cdot \left( \mu_{i} \cdot e^{- \mu_{i}/k} \right) \cdot x_{i,j}}\]