Asymptotic Inference for a Change-Point Poisson Process

Easily implemented asymptotic off-line procedures for the change-point Poisson process with $\lambda(t)$, the intensity at time $t$, equal to $\lambda_1$ if $t \leq \tau$ and to $\lambda_2$ if $t > \tau$, are developed. They may also be applied to a problem of estimation of the location of a discontinuity in density discussed by Chernoff and Rubin (1956). A test for change is noted, a test of the hypothesis that $\tau = \tau_0$ is proposed, and point and interval estimates of $\tau, \lambda_1$, and $\lambda_2$ are provided. The small-sample performance of the proposed procedures is studied using simulation, and an example is given.