Algorithms for Point Processes Analysis

A time point process can be defined either by the statistical properties of the time intervals between successive points or by those of the number of points in arbitrary time intervals. There are mathematical expressions to link up these two points of view, but they are in many cases too complicated to be used in practice. In this paper we present an algorithmic procedure to obtain the number of points of a stationary point process recorded in some time intervals by processing the values of the distances between successive points. We present some results concerning the statistical analysis of these numbers of points and when analytical calculations are possible the experimental results obtained with our algorithms are in excellent agreement with those predicted by the theory. Some properties of point processes in which theoretical calculations are almost impossible are also presented. Some key words. Point processes, renewal processes, lifetime, counting. Unité mixte de recherche (UMR 8506) du Centre national de la recherche scientifique (CNRS), de l’École supérieure d’électricité (Suplec) et de l’Université de Paris-Sud 11 (UPS). 1 ha l-0 07 93 38 5, v er si on 1 22 F eb 2 01 3 Author manuscript, published in "Communications in Statistics Simulation and Computation 42, 1 (2013) 90-106" DOI : 10.1080/03610918.2011.633197