J-function for inhomogeneous spatio-temporal point processes
Journal article, 2015

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.

(reduced Palm measure) generating functional



inhomogeneous spatio-temporal point process

location-dependent thinning of hard core model

intensity-reweighted moment sta- tionarity

Papangelou conditional intensity

n-point correlation function

Poisson process

log- Gaussian Cox process


Ottmar Cronie

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Marie Colette N.M. Van Lieshout

Scandinavian Journal of Statistics

0303-6898 (ISSN) 1467-9469 (eISSN)

Vol. 2 562-579

Subject Categories

Probability Theory and Statistics

Mathematical Analysis



More information