Testing Whether Interpenetration is Possible for the Grains of a Random Set

Abstract

In this article we investigate the following problem: Find an appropriate test which based on a spatially restricted observation of a (generalized) germ-grain model allows to decide whether interpretration of the grains of this set is possible or not. For two special hypotheses different test statistics are proposed which are useful under particular interpretations of the problem. Some of their properties are given. A conditional test based on the generalized likelihood ratio principle leads to a very simple determination of the critical values and of the power function.

Keywords:

• AMS 1980 subject classifications
• Primary 60D05
• secondary 62M30

Keywords:

• Generalized germ-grain models
• interpretation
• marked point processes
• global tests and conditional tests