Kybernetika 55 no. 5, 802-808, 2019

A note on discriminating Poisson processes from other point processes with stationary inter arrival times

Gusztáv Morvai and Benjamin WeissDOI: 10.14736/kyb-2019-5-0802

Abstract:

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.

Keywords:

Point processes

Classification:

60G55

paper.pdf

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