Non-parametric indices of dependence between types for inhomogeneous multivariate random closed sets.

We propose new summary statistics to quantify the correlation between the components in coverage-reweighted moment stationary multivariate random closed sets. They are defined in terms of the coverage-reweighted cumulant densities and under stationarity reduce to the reduced cross correlation measure and cross hitting functional proposed by Stoyan and Ohser (1982). Unbiased estimators are given for all statistics and applied to simulations of a bivariate germ-grain model.