With DispersionEstimatorFunction->"PearsonChiSquare", the estimator is where n is the number of data points, p is the number of parameters, and v is the variance function for the distribution.
Non-default values can be used to model overdispersion in "Binomial" and "Poisson" models.
With the setting DispersionEstimatorFunction->f, the common dispersion is estimated by where y={y1, y2, ...} is the list of observations, is the list of predicted values and w={w1, w2, ...} is the list of weights for the measurements yi.