We propose the goodness-of-fit test for inhomogeneous Poisson processes with unknown scale parameter. A test statistic of the Anderson-Darling type is proposed and its asymptotic behavior is studied when the unknown parameter is estimated using the maximum likelihood estimator. We show that under null hypothesis, the limit distribution of this statistic does not depend on unknown parameter. Furthermore, we establish the consistency of the test against the alternative hypothesis.

inhomogeneous Poisson process, parametric basic hypothesis, Anderson-Darling type test, maximum likelihood estimator, asymptotically parameter free test, scale parameter

Received: August 27, 2024; Revised: December 16, 2024; Accepted: February 12, 2025; Published: March 25, 2025

How to cite this article: H. G. Izaddine, D. Diakhaté, A. D. Rafiou and A. S. Dabye, Goodness-of-fit test for Poisson processes with a scale parameter, Far East Journal of Theoretical Statistics 69(2) (2025), 129‑153. https://doi.org/10.17654/0972086325006

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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