Modelling point patterns with the Ivanoff–Merzbach renewal process

Abstract This paper demonstrates how to apply the Ivanoff–Merzbach renewal process (Ivanoff and Merzbach, 2006 ; Ivanoff, 2008 ) to the modelling of environmental and other forms of point process data. The model is explored via simulation, focusing on two special cases. Maximum likelihood estimation of model parameters is described and demonstrated for these cases. The methods are applied to a point pattern related to human settlement patterns and to a point pattern describing the locations of a species of pine. Copyright © 2009 John Wiley & Sons, Ltd.