Moment data can be analytically completed

Gavriliadis, PN; Athanassoulis, GA

dc.contributor.author	Gavriliadis, PN	en
dc.contributor.author	Athanassoulis, GA	en
dc.date.accessioned	2014-03-01T01:19:18Z
dc.date.available	2014-03-01T01:19:18Z
dc.date.issued	2003	en
dc.identifier.issn	0266-8920	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15405
dc.subject	Hausdorff moment problem	en
dc.subject	Moment bounds	en
dc.subject	Non-parametric model	en
dc.subject	Probability density function	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.classification	Statistics & Probability	en
dc.subject.other	Algorithms	en
dc.subject.other	Convergence of numerical methods	en
dc.subject.other	Mathematical models	en
dc.subject.other	Optimization	en
dc.subject.other	Probability density function	en
dc.subject.other	Problem solving	en
dc.subject.other	Hausdorff moment problem	en
dc.subject.other	Continuum mechanics	en
dc.title	Moment data can be analytically completed	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.probengmech.2003.07.001	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.probengmech.2003.07.001	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	When an unknown (target) probability density function (pdf) is to be reconstructed from its moments with the aid of a multiparametric (or semi-parametric) representation model, a large number of constraints (moment equations) is needed, usually larger than the unknown parameters. However, there is a strong belief, expressed by various authors, see Fasino D, Inglese G (Rendiconti dell' Istituto di Matematica dell' Universita di Trieste XXVIII (1996) 183], and French JB [In: Dalton BJ, et al., Theory and application of moments problems in many-fermion systems (1979) 1], that most of the information defining a compactly supported pdf is usually contained in its first few moments. In addition, numerical experimentation has shown [Probab Engng Mech 17 (2002) 273] that the variation of the reconstructed pdf when higher-order moments vary within the recursively defined moment bounds, is weak, becoming insignificant as the moment order N increases. Based on these observations, we propose a method for extending a set of given moments, in cases that they are insufficient for solving the Hausdorff moment problem using a multiparametric model. Additional moments, compatible with the given ones, are obtained by exploiting upper and lower moment bounds. Then, two sequences of 'dual' (upper and lower) approximant pdfs are constructed, along with an easily realizable criterion of mutual convergence. The numerical performance and consistency of the solution algorithm have been illustrated for unimodal and bimodal pdfs. (C) 2003 Elsevier Ltd. All rights reserved.	en
heal.publisher	ELSEVIER SCI LTD	en
heal.journalName	Probabilistic Engineering Mechanics	en
dc.identifier.doi	10.1016/j.probengmech.2003.07.001	en
dc.identifier.isi	ISI:000186903800006	en
dc.identifier.volume	18	en
dc.identifier.issue	4	en
dc.identifier.spage	329	en
dc.identifier.epage	338	en