Maximum Entropy Reconstruction for Discrete Distributions with Unbounded Support

TL;DR

This paper introduces a maximum entropy method with adaptive support approximation to reconstruct one-dimensional discrete distributions, effectively capturing the main probability mass region.

Contribution

It presents a novel numerical technique for adaptive support approximation in maximum entropy reconstruction of discrete distributions.

Findings

Effective reconstruction of distributions with unbounded support.

Improved accuracy in capturing main probability mass regions.

Demonstrated applicability to classical moment problems.

Abstract

The classical problem of moments is addressed by the maximum entropy approach for one-dimensional discrete distributions. The numerical technique of adaptive support approximation is proposed to reconstruct the distributions in the region where the main part of probability mass is located.