Geodesic
A note on discriminating Poisson processes from other point processes with stationary inter arrival times
Kybernetika, Tome 55 (2019) no. 5, pp. 802-808
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We give a universal discrimination procedure for determining if a sample point drawn from an ergodic and stationary simple point process on the line with finite intensity comes from a homogeneous Poisson process with an unknown parameter. Presented with the sample on the interval $[0,t]$ the discrimination procedure $g_t$, which is a function of the finite subsets of $[0,t]$, will almost surely eventually stabilize on either POISSON or NOTPOISSON with the first alternative occurring if and only if the process is indeed homogeneous Poisson. The procedure is based on a universal discrimination procedure for the independence of a discrete time series based on the observation of a sequence of outputs of this time series.
We give a universal discrimination procedure for determining if a sample point drawn from an ergodic and stationary simple point process on the line with finite intensity comes from a homogeneous Poisson process with an unknown parameter. Presented with the sample on the interval $[0,t]$ the discrimination procedure $g_t$, which is a function of the finite subsets of $[0,t]$, will almost surely eventually stabilize on either POISSON or NOTPOISSON with the first alternative occurring if and only if the process is indeed homogeneous Poisson. The procedure is based on a universal discrimination procedure for the independence of a discrete time series based on the observation of a sequence of outputs of this time series.
DOI : 10.14736/kyb-2019-5-0802
Classification : 60G55
Keywords: Point processes 
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Morvai, Gusztáv; Weiss, Benjamin. A note on discriminating Poisson processes from other point processes with stationary inter arrival times. Kybernetika, Tome 55 (2019) no. 5, pp. 802-808. doi: 10.14736/kyb-2019-5-0802

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