Maximun entropy in the discrete generalized moment problem

Abstract

The recovering of  a discrete probability distribution taking on a countable values, when only partial information is available, is considered. The partial information is provided by a finite number of available  generalized moments, so that the problem of recovering resorts to an underdetermined generalized moment problem. Maximun  entropy method is invoked in choosing  the analytical form of the approximant distribution having the same moments.

It is proved that except the cases in wich M=2 or M=3 generalized moments are assigned, the necessary and sufficient conditions for the existence of a maximun entropy distribution are identical to the ones of the reduced moment problem.