Asymptotic Inference for a Change-Point Poisson Process

Easily implemented asymptotic off-line procedures for the change-point Poisson process with λ(t), the intensity at time t, equal to λ₁ if t ≤ τ and to λ₂ if t > τ, 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 τ = τ₀ is proposed, and point and interval estimates of τ, λ₁, and λ₂ are provided. The small-sample performance of the proposed procedures is studied using simulation, and an example is given.