Poisson deviance
= Poisson deviance
For independent Poisson observations with fitted means $\widehat\mu_i$, the deviance from the saturated model is
$$
D=2\sum_i\left\{y_i\log\frac{y_i}{\widehat\mu_i}-(y_i-\widehat\mu_i)\right\},
$$
with $0\log0=0$.