Experimental Design and Statistical Inference for Cluster Point Processes – with Applications to the Fruit Dispersion of Anemochorous Forest Trees

Abstract

Abstract This paper deals with experimental design and statistical inference for cluster point processes. The results are applied to fruit dispersion models of forest trees where the corresponding design of experiments is given by the positions of the traps containing the collected fruits. It is shown that consideration of anisotropic behaviour can lead to more realistic models. Modelling interactivity effects between trees seems to be of great interest. It is shown that an approach based on ordered weighted averages yields an notable improvement of model quality. The mathematical background of such models (Choquet integral, fuzzy measures) is sketched in the appendix. Finally, results for choosing a D‐optimal sub‐design are presented.