We propose parameter estimators for a Bellman-Harris branching process (c.f.[2],[5]; Chapter VI) which require only an enumeration of all living members' ages at the present time t. Previous estimators (c.f.[4] and [9]) require a complete or partial historical record of the process during some interval of time contained in [0, t]. When the complete history of the process is available, the likelihood factors into a component for splits and one for the possibly right censored life lengths [6] so the usual estimation procedures apply. Secondly, we obtain our estimates by jointly estimating the mean number of splits m and the life distribution G(.), whereas most other published works have treated these two problems separately. More particularly, we restrict our attention to parametric families of life distributions G(a) e G(-; 0) and estimate 8 and m
Recall that, under a Bellman-Harris branching process, a parent lives a random length of time and at death produces a random number of offsprings.
The parent lifetimes are all assumed to be independent identically distributed random variables from the common cumulative distribution G(.), the number of offsprings per parent are all assumed to be independent identically distributed random variables from the common probability distribution {pj}y=o,or and all lifetimes and number of offsprings are mutually independent.