TABLE I.

Exponential family and link functions

Distribution	$\theta$	$\eta$	$T(\mathbf{x})$	$A(\eta )$	g
Bernouli	$p$	$\text{log}\frac{p}{1-p}$	x	$\text{log}(1+e^{\eta })$	logit
Binomial	$p$	$\text{log}\frac{p}{1-p}$	x	$n\text{log}(1+e^{\eta })$	logit
Negative Binomial	$p$	$\text{log}p$	x	$-r\text{log}(1-e^{\eta })$	logit
Poisson	$\lambda$	$\text{log}\lambda$	x	$e^{\eta }$	log
Gaussian	[$\mu$, ${\sigma }^2$]	[$\mu ∕{\sigma }^2$, $-1∕2{\sigma }^2$]	[$x$, $x^2$]	${\mu }^2∕2$	identity