Changing time of simple continuous-time Markov counting processes by independent unit-rate Poisson processes results in Markov counting processes for which we provide closed-form transition rates via composition of trajectories and with which we construct novel, simpler infinitesimally...

We provide a multivariate extension of a recent result for univariate Markov counting processes: necessity and sufficiency of compoundness for infinitesimal over-dispersion. As an illustration, we show that infinitesimally over-dispersed epidemiological SIR-type compartment models must rely on...

An empirical Bayes approach is used to predict future values of n and x generated by a two-stage Poisson([lambda])-multinomial(p) process with an arbitrary compounding distribution on ([lambda], p). Asymptotic variances of the predictors are obtained. The approach is also useful in examining the...