The discrete moment problem and linear programming
type: Item
instance of: scholarly article
title: The discrete moment problem and linear programming
zbMATH Open document ID: 0712.90045
DOI: 10.1016/0166-218X(90)90068-N
published in: Discrete Applied Mathematics
publication date: 1990-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 90C90
Mathematics Subject Classification ID: 65C99
zbMATH DE Number: 4172736
zbMATH Keywords: classical moment problem
zbMATH Keywords: probability measure
zbMATH Keywords: lower and upper bounds
zbMATH Keywords: discrete random variables
zbMATH Keywords: power moment problem
author: András Prékopa
reviewed by: I. M. Stancu-Minasian
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4172736