Multinomial deviance
= Multinomial deviance
{title2=$G^2=2\sum_{i:y_i>0}y_i\log[y_i/(Np_i)]$}
For counts with a <multinomial distribution>, this is twice the log likelihood ratio of the saturated cell-probability estimate to fixed probabilities $p_i$. Zero-count terms have limiting value zero. Simulation under the specified probabilities gives a direct reference distribution when asymptotic approximations are unsuitable.