<abstract>

An index for characterizing the separation of two distributions is introduced. It is applied to assessing whether mixture components are clusters. A related property of being a satellite and a partial ordering of the components are defined. A sequence of clustering structures is defined for a finite mixture with a continuum of thresholds that qualify a cluster. The approach is suitable for outcomes with arbitrary univariate or multivariate distributions and their mixtures. The properties of the index are explored by simulations and on examples.

</abstract>