Hausdorff moment problem and fractional moments
type: Item
instance of: scholarly article
title: Hausdorff moment problem and fractional moments
zbMATH Open document ID: 1198.44005
published in: Applied Mathematics and Computation
publication date: 2010-07-19T00:00:00Z
review text: In probabilistic terms, the Hausdorff moment problem means to recover an unknown probability density function \(f\in L^2[0,1]\) from the knowledge of its associated sequence \(\{\mu_j\}^M_{j=0}\) of integer moments, that is, \(\mu_j=\int_0^1x^jf(x),j\geq0,\mu_0=1\). The authors propose a solution to the Hausdorff moment problem using fractional moments, appropriately chosen, of the form \(\int_0^1x^{\alpha}f(x)dx\), with \(\alpha\in\mathbb R^+\). Fractional moments are computed from integer moments via so-called centered moments. They are used in turn to solve finite Hausdorff moment problems by means of a maximum entropy technique, and in authors' opinion, they represent a remedy to ill-conditioning coming from a high number of integer moments needed by the recovering procedure.
reviewed by: Florian-Horia Vasilescu
Mathematics Subject Classification ID: 44A60
zbMATH DE Number: 5757598
zbMATH Keywords: Hausdorff moment problems
zbMATH Keywords: Hankel matrices
zbMATH Keywords: integer moments, centered moments
zbMATH Keywords: fractional moments
zbMATH Keywords: maximum entropy
zbMATH Keywords: ill-conditioning
author: Henryk Gzyl
author: Aldo Tagliani
describes a project that uses: MPFUN
MaRDI profile type: Publication
full work available at URL: j.amc.2010.04.059
OpenAlex ID: W4251792106
cites work: Recovering a function from a finite number of moments
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cites work: Hausdorff moment problem and maximum entropy: A unified approach
DOI: 10.1016/J.AMC.2010.04.059
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description: scientific article; zbMATH DE number 5757598