https://hal-centralesupelec.archives-ouvertes.fr/hal-03575440Picinbono, BernardBernardPicinbonoL2S - Laboratoire des signaux et systèmes - CentraleSupélec - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueCoincidence functions and Bartlett spectra of point processesFonctions de coïncidences et spectres de Bartlett de processus ponctuelsHAL CCSD2021Point processesPoisson processesrenewal processescoincidence function measurementBartlett spectrumshot noisecounting methods[SPI] Engineering Sciences [physics][STAT] Statistics [stat]Picinbono, Bernard2022-02-15 15:10:192023-03-09 10:30:172022-02-24 09:56:56enJournal articleshttps://hal-centralesupelec.archives-ouvertes.fr/hal-03575440/document10.1080/03610918.2019.1680693application/pdf1The second order statistical properties of time point processes (PP) are described by the time coincidence function (CF) and the frequency Bartlett spectrum (BS). For PPs recorded by pulses appearing at random time instants, as in photodetection experiments, the CF can be measured by various physical devices showing in particular the famous bunching effect of photons. On the other hand, for PPs recorded by the intervals between successive points (lifetimes), especially for renewal processes, there is no usual procedure for the estimation of the CF, and the aim of this paper is to describe an approach of this problem. The starting point is a mathematical relation between the CF and the set of probabilities density functions of the lifetimes of any order of the PP. As a consequence the CF can be obtained by processing the results of the multiple normalized histograms of these lifetimes. In the cases, relatively rare, where the mathematical expression of the CF is known in closed form, the correct behavior of the procedure is verified by an experimental analysis of simulated data. The method is extended in order to verify the relationship between the CF and the BS.