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Independence of thinned processes characterizes the Poisson process: an elementary proof and a statistical application. (English) Zbl 1119.62089
Summary: Let \(N, N_{1}\) and \(N_{2}\) be point processes such that \(N_{1}\) is obtained from \(N\) by homogeneous independent thinning and \(N_{2}=N - N _{1}\). We give a new elementary proof that \(N_{1}\) and \(N_{2}\) are independent if and only if \(N\) is a Poisson point process. We also present an application of this result to test if a homogeneous point process is a Poisson point process.

62M30 Inference from spatial processes
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
62M07 Non-Markovian processes: hypothesis testing
62P10 Applications of statistics to biology and medical sciences; meta analysis
Full Text: DOI arXiv
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