A J ‐function for Inhomogeneous Spatio‐temporal Point Processes

We propose a new summary statistic for inhomogeneous intensity‐reweighted moment stationarity spatio‐temporal point processes. The statistic is defined in terms of the n ‐point correlation functions of the point process, and it generalizes the J ‐function when stationarity is assumed. We show that our statistic can be represented in terms of the generating functional and that it is related to the spatio‐temporal K ‐function. We further discuss its explicit form under some specific model assumptions and derive ratio‐unbiased estimators. We finally illustrate the use of our statistic in practice. © 2014 Board of the Foundation of the Scandinavian Journal of Statistics