  An extension of the Hawkes model where the productivity is variable is
considered. In particular, the case is considered where each point may have its
own productivity and a simple analytic formula is derived for the maximum
likelihood estimators of these productivities. This estimator is compared with
an empirical estimator and ways are explored of stabilizing both estimators by
lower truncating, smoothing, and rescaling the estimates. Properties of the
estimators are explored in simulations, and the methods are applied to
seismological and epidemic datasets to show and quantify substantial variation
in productivity.
