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

Gusztáv Morvai; Benjamin Weiss

Kybernetika (2019)

- Volume: 55, Issue: 5, page 802-808
- ISSN: 0023-5954

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topMorvai, Gusztáv, and Weiss, Benjamin. "A note on discriminating Poisson processes from other point processes with stationary inter arrival times." Kybernetika 55.5 (2019): 802-808. <http://eudml.org/doc/295069>.

@article{Morvai2019,

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.},

author = {Morvai, Gusztáv, Weiss, Benjamin},

journal = {Kybernetika},

keywords = {Point processes},

language = {eng},

number = {5},

pages = {802-808},

publisher = {Institute of Information Theory and Automation AS CR},

title = {A note on discriminating Poisson processes from other point processes with stationary inter arrival times},

url = {http://eudml.org/doc/295069},

volume = {55},

year = {2019},

}

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

PB - Institute of Information Theory and Automation AS CR

VL - 55

IS - 5

SP - 802

EP - 808

AB - 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.

LA - eng

KW - Point processes

UR - http://eudml.org/doc/295069

ER -

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