Combinatorial problems according to conditions on fitting a constructively defined multivariate gamma distribution to empirical data

The main goal of this paper is to give new results according to fitting the multivariate gamma distribution to empirical data. In an earlier paper necessary conditions of fitting were given and the sufficiency of these conditions was proved for dimension 4. For higher dimensions the question of sufficiency of the necessary conditions remained an open question. In this paper we formulate further necessary conditions. This way we prove that the necessary conditions given earlier are not sufficient. Using the more efficient computational tools we are able now to give the sufficient conditions for dimensions 5 and 6 as well. However, for higher dimensions we have only necessary conditions and the sufficiency of these conditions remains an open question.