Independence of thinned processes characterizes the Poisson process: an elementary proof and a statistical application
نویسندگان
چکیده
Let N , N1 and N2 be point processes such that N1 is obtained from N by homogeneous independent thinning and N2 = N −N1. We give a new elementary proof that N1 and N2 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.
منابع مشابه
Detection of spatial pattern through independence of thinned processes
Let N , N1 and N2 be point processes such that N1 is obtained from N by homogeneous independent thinning and N2 = N −N1. We give a new elementary proof that N1 and N2 are independent if and only if N is a Poisson point process. We present some applications of this result to test if a homogeneous point process is a Poisson point process.
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