We propose new summary statistics to quantify the association between the components in coverage-reweighted moment stationary multivariate random sets and measures. They are defined in terms of the coverage-reweighted cumulant densities and extend classic functional statistics for stationary random closed sets. We study the relations between these statistics and evaluate them explicitly for a range of models. Unbiased estimators are given for all statistics and applied to simulated examples and to tropical rain forest data.
- Coverage-reweighted moment stationarity
- Cross hitting functional
- Empty space function
- Moment measure
- Reduced cross correlation measure
- Spherical contact distribution
- Bivariate random measure