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.

Full paper (PDF)

This article in mathematical reviews.