Second-order intensity-reweighted stationary isotropic and geometric anisotropic spatial point processes, with a view to Cox processes

For statistical analysis of spatial point patterns, it is often assumed that the underlying spatial point process is second-order stationary. Moreover, the pair correlation function is often assumed to be isotropic due to simpler interpretation and ease of analysis. However, in many applications second-order stationarity or isotropy of the pair correlation function is known not to be satisfied. For instance, the distribution of plant seedling locations often exhibits spatial inhomogeneity due to diffeerent ground conditions and anisotropy due to factors such as prevailing wind direction. Failure to account for spatial inhomogeneity and directional inhomogeneity can result in erroneous inferences. This research extends work by Castelloe (1998) to second-order intensity reweighted stationary spatial point processes with an elliptical pair correlation function. Thereby it is possible to model spatial inhomogeneity, and the assumption that the pair correlation function is elliptical is useful for descriptive purposes of anisotropy.