Estimating the Change in a Renewal Process When the Data are Counts

Abstract

Let X ₁, …, X _n be the interarrival times of a renewal process. A change-point is said to occur in this sequence if X ₁, …, X _τ have a common distribution F while X _{τ +1}, … X _n have distribution G, with F ≠ G. Usually τ is unknown, and must be estimated from the data. In a renewal process, it is sometimes not possible to observe the renewal times accurately. Instead, the data consist of counts of renewals in successive time intervals. This paper investigates methods of estimation of the change-point when the only data available are these counts. Examples and simulations are included.

Keywords:

• change-point
• renewal process
• Poisson sampling