Moment information for probability distributions, without solving the moment problem, II: Main-mass, tails and shape approximation

Gavriliadis, PN; Athanassoulis, GA

dc.contributor.author	Gavriliadis, PN	en
dc.contributor.author	Athanassoulis, GA	en
dc.date.accessioned	2014-03-01T01:31:15Z
dc.date.available	2014-03-01T01:31:15Z
dc.date.issued	2009	en
dc.identifier.issn	0377-0427	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19758
dc.subject	Approximation	en
dc.subject	Chebyshev-Stieltjes-Markov inequality	en
dc.subject	Christoffel function	en
dc.subject	Distribution functions	en
dc.subject	Moments	en
dc.subject	Tail	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Approximation	en
dc.subject.other	Chebyshev-Stieltjes-Markov inequality	en
dc.subject.other	Christoffel function	en
dc.subject.other	Moments	en
dc.subject.other	Tail	en
dc.subject.other	Chebyshev approximation	en
dc.subject.other	Probability density function	en
dc.subject.other	Targets	en
dc.subject.other	Distribution functions	en
dc.title	Moment information for probability distributions, without solving the moment problem, II: Main-mass, tails and shape approximation	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.cam.2008.10.011	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.cam.2008.10.011	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	How much information does a small number of moments carry about the unknown distribution function? Is it possible to explicitly obtain from these moments some useful information, e.g., about the support, the modality, the general shape, or the tails of a distribution, without going into a detailed numerical solution of the moment problem? In this, previous and subsequent papers, clear and easy to implement answers will be given to some questions of this type. First, the question of how to distinguish between the main-mass interval and the tail regions, in the case we know only a number of moments of the target distribution function, will be addressed. The answer to this question is based on a version of the Chebyshev-Stieltjes-Markov inequality, which provides us with upper and lower, moment-based, bounds for the target distribution. Then, exploiting existing asymptotic results in the main-mass region, an explicit, moment-based approximation of the target probability density function is provided. Although the latter cannot be considered, in general, as a satisfactory solution, it can always serve as an initial approximation in any iterative scheme for the numerical solution of the moment problem. Numerical results illustrating all the theoretical statements are also presented. (C) 2008 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Journal of Computational and Applied Mathematics	en
dc.identifier.doi	10.1016/j.cam.2008.10.011	en
dc.identifier.isi	ISI:000266511500002	en
dc.identifier.volume	229	en
dc.identifier.issue	1	en
dc.identifier.spage	7	en
dc.identifier.epage	15	en