Printed in Great Britain On parametric estimation for mortal branching processes

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 data for Europe. Some key words: Age-dependent branching process; Borel-Tanner distribution; Epidemic model; Information; Maximum likelihood estimation; Minimum variance unbiased estimation; Power series distribution; Smallpox in Europe; Sufficient statistic