On parametric estimation for mortal branching processes

SUMMARY If the offspring distribution in a branching process is a power series distribution, then, conditional on extinction, the total number of descendants for the process also has a power series distribution. For this case the estimation of the parameter and of the mean of the offspring distribution is considered, using the method of maximum likelihood and minimum variance unbiasedness. The minimum variance unbiased estimator for the variance of the estimator of the parameter is also given. The results are applied to smallpox datafor Europe.