Independence of thinned processes characterizes the Poisson process: An elementary proof and a statistical application

• Autores: R. M. Assunção, Pablo A. Ferrari
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 16, Nº. 2, 2007, págs. 333-345
• Idioma: inglés
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• Resumen

  • 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.