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.
@article{10_14736_kyb_2019_5_0802,
author = {Morvai, Guszt\'av and Weiss, Benjamin},
title = {A note on discriminating {Poisson} processes from other point processes with stationary inter arrival times},
journal = {Kybernetika},
pages = {802--808},
publisher = {mathdoc},
volume = {55},
number = {5},
year = {2019},
doi = {10.14736/kyb-2019-5-0802},
mrnumber = {4055577},
zbl = {07177917},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2019-5-0802/}
}
TY - JOUR AU - Morvai, Gusztáv AU - Weiss, Benjamin TI - A note on discriminating Poisson processes from other point processes with stationary inter arrival times JO - Kybernetika PY - 2019 SP - 802 EP - 808 VL - 55 IS - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2019-5-0802/ DO - 10.14736/kyb-2019-5-0802 LA - en ID - 10_14736_kyb_2019_5_0802 ER -
%0 Journal Article %A Morvai, Gusztáv %A Weiss, Benjamin %T A note on discriminating Poisson processes from other point processes with stationary inter arrival times %J Kybernetika %D 2019 %P 802-808 %V 55 %N 5 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2019-5-0802/ %R 10.14736/kyb-2019-5-0802 %G en %F 10_14736_kyb_2019_5_0802
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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