ON MAXIMUM-ENTROPY DISTRIBUTIONS OF NONNEGATIVE RANDOM VARIABLES WITH CONDITIONAL-ADDITIVE STRUCTURE UNDER INEQUALITY CONSTRAINTS

摘要

The Maximum Entropy Principle is used to find distributions of an integer non-negative random variable with conditional-additive structure when some bounds for the conditional expectations of its components are known. We obtain that the components of these distributions can be blocked in rows that form a general matrix-geometric sequence. Finally, we examine the more difficult case when upper bounds for second-order moments of components are given.