Hausdorff moment problem via fractional moments

TL;DR

This paper presents an efficient maximum entropy method to reconstruct probability densities from fractional moments derived from ordinary moments, ensuring convergence in entropy and accurate expectation calculations.

Contribution

It introduces a novel approach to compute fractional moments explicitly from ordinary moments, enabling density reconstruction with proven entropy convergence.

Findings

Density approximation converges in entropy to the true density.

Method effectively computes fractional moments from ordinary moments.

Reconstructed densities are useful for expectation calculations.

Abstract

We outline an efficient method for the reconstruction of a probability density function from the knowledge of its infinite sequence of ordinary moments. The approximate density is obtained resorting to maximum entropy technique, under the constraint of some fractional moments. The latter ones are obtained explicitly in terms of the infinite sequence of given ordinary moments. It is proved that the approximate density converges in entropy to the underlying density, so that it demonstrates to be useful for calculating expected values.