Discrete probability distributions in the generalized moment problem

摘要

The discrete maximum entropy probability distribution which can take on a finite number of values and whose first generalized moments are assigned, is considered. It is proved that the necessary and sufficient conditions for the existence of a maximum entropy solution are identical to the general ones for the finite moment problem. The entropy decreasing by adding one more moment is studied. Instability of the distribution to be recovered is proved when an increasing number of moments is used.