Note on the Anderson–Darling type test for Poisson processes with shift and scale parameters

A.D. Rafiou, S. Deme, H.G. Izaddine and A.S. Dabye

Statistics & Probability Letters, 2025, vol. 226, issue C

Abstract: We present a goodness-of-fit test designed for inhomogeneous Poisson processes where the scale and shift parameters are unknown. Our approach involves a test statistic of Anderson–Darling type, and we analyze its asymptotic properties. We prove that, under the null hypothesis, the asymptotic distribution of this statistic is independent of the unknown parameters. Additionally, we establish that the Anderson–Darling type test is consistent for the alternative hypothesis.

Keywords: Inhomogeneous poisson process; Anderson–darling test; Scale and shift parameters; Asymptotically parameter free test (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2025.110479

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