The truncated Hausdorff moment problem solved by using kernel density functions

Athanassoulis, GA; Gavriliadis, PN

dc.contributor.author	Athanassoulis, GA	en
dc.contributor.author	Gavriliadis, PN	en
dc.date.accessioned	2014-03-01T01:18:26Z
dc.date.available	2014-03-01T01:18:26Z
dc.date.issued	2002	en
dc.identifier.issn	0266-8920	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15005
dc.subject	Ill-posed problem	en
dc.subject	Kernel density function	en
dc.subject	Probability density function	en
dc.subject	Truncated Hausdorff moment problem	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	Constraint theory	en
dc.subject.other	Convergence of numerical methods	en
dc.subject.other	Least squares approximations	en
dc.subject.other	Probability density function	en
dc.subject.other	Kernel density functions	en
dc.subject.other	Problem solving	en
dc.title	The truncated Hausdorff moment problem solved by using kernel density functions	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0266-8920(02)00012-7	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0266-8920(02)00012-7	en
heal.language	English	en
heal.publicationDate	2002	en
heal.abstract	In this work, the problem of an efficient representation and its exploitation to the approximate determination of a compactly supported, continuous probability density function (pdf) from a finite number of its moments is addressed. The representation used is a finite superposition of kernel density functions. This representation preserves positivity and can approximate any continuous pdf as closely as it is required. The classical theory of the Hausdorff moment problem is reviewed in order to make clear how the theoretical results as, e.g. the moment bounds, can be exploited in the numerical procedure. Various difficulties arising from the well-known ill-posedness of the numerical moment problem have been identified and solved. The kernel coefficients of the pdf expansion are calculated by solving a constrained, non-negative least-square problem. The consistency, numerical convergence and robustness of the solution algorithm have been illustrated by numerical examples with unimodal and bimodal pdfs. Although this paper is restricted to univariate, compactly supported pdfs, the method can be extended to general pdfs either univariate or multivariate, with finite or infinite support. (C) 2002 Published by Elsevier Science Ltd.	en
heal.publisher	ELSEVIER SCI LTD	en
heal.journalName	Probabilistic Engineering Mechanics	en
dc.identifier.doi	10.1016/S0266-8920(02)00012-7	en
dc.identifier.isi	ISI:000177177800007	en
dc.identifier.volume	17	en
dc.identifier.issue	3	en
dc.identifier.spage	273	en
dc.identifier.epage	291	en