The discrete moment problem and linear programming
The classical moment problem can be described as: For a given subset \(S\) of \(R\), find a probability measure on \(S\) with prescribed first \(m\) moments, which minimizes the expectation of a given criterion function on \(S\). In this paper moment problems with finite and preassigned support with respect to the probability distribution are formulated and used to obtain sharp lower and upper bounds for unknown probabilities and expectations of convex functions of discrete random variables. The bounds are optimum values of special linear programming problems. In Section 2 some basic notions and theorems are given. In Section 3 the dual feasible bases of the linear programming problems involved are characterized in case of the power and binomial moment problems. In Section 4 generalizations and algorithmic solutions of the problems are mentioned. In Section 5 the power moment problem is analysed in more detail and closed form bounds are derived for probabilities, expectations and higher order binomial moments.
scientific article; zbMATH DE number 4172736