  This paper concerns a method of testing equality of distribution of random
convex compact sets and the way how to use the test to distinguish between two
realisations of general random sets. The family of metrics on the space of
distributions of random convex compact sets is constructed using the theory of
N-distances and characteristic functions of random convex compact sets.
Further, the approximation of the metrics through its finite dimensional
counterparts is proposed, which lead to a new statistical test for testing
equality in distribution of two random convex compact sets. Then, it is
described how to approximate a realisation of a general random set by a union
of convex compact sets, and it is shown how to determine whether two
realisations of general random sets come from the same process using the
constructed test. The procedure is justified by an extensive simulation study.
