The Relative Moments Method

Keywords: aggregation, homogeneity, cluster, mulvariate distribution, distance data, metric space

Abstract: A method for comparison of probability distributions on metric spaces (Euclidean spaces in particular) will be presented in this talk. This method is based on the concepts of relative moments and relative aggregation coefficients (RAC), which are real-valued summary descriptors of probability distributions. It will be shown how RAC characterizes (relative) homogeneity and equality of two probability distributions, and how RAC can be used in statistical inference. An application to the test of spatial homogeneity as an alternative to scan statistics, and consistent estimation of RAC (as an index measuring nonhomogeneity) will be presented.