**Sankhya: The Indian Journal of Statistics**

1995, Volume 57, Series A, Pt. 3, pp. 486--499

** ESTIMATING THE NUMBER OF COMPONENTS OF A SYSTEM OF SUPERIMPOSED RENEWAL PROCESS**

By

ANUP DEWANJI, *Indian Statistical Institute*

TAPAN K. NAYAK, *George Washington University*

and

PRANAB K. SEN, *University of North Carolina*

SUMMARY. Consider a superposition of an unknown number, $\nu$, of independent, identically distributed renewal processes and supose that whenever an event occurs, the component process in which it occurred can be identified. We discuss maximum likelihood estimation of $\nu$ and the parameters of the common renewal density based on the data generated over a fixed interval of time. Some asymptotic properties of these methods are discussed. In particular, we prove asymptotic normality of a class of estimators under quite general conditions.

*AMS (1991) subject classification.* 62M09, 62F12.

*Key words and phrases.* Renewal process, marked point process, consistency, maximum likelihood.