Please use this identifier to cite or link to this item:
Full metadata record
DC FieldValueLanguage
dc.contributor.authorVladik Kreinovichen_US
dc.contributor.authorHung T. Nguyenen_US
dc.contributor.authorSongsak Sriboonchittaen_US
dc.contributor.authorOlga Koshelevaen_US
dc.description.abstract© Springer International Publishing Switzerland 2015. A natural way to represent a 1-D probability distribution is to store its cumulative distribution function (cdf) F(x) = Prob(X ≤ x). When several random variables X1,..., Xn are independent, the corresponding cdfs F1(x1),..., Fn(xn) provide a complete description of their joint distribution. In practice, there is usually some dependence between the variables, so, in addition to the marginals Fi(xi), we also need to provide an additional information about the joint distribution of the given variables. It is possible to represent this joint distribution by a multi-D cdf F(x1,..., xn) = Prob(X1 ≤ x1 &... &Xn ≤ xn), but this will lead to duplication-since marginals can be reconstructed from the joint cdf-and duplication is a waste of computer space. It is therefore desirable to come up with a duplication-free representation which would still allow us to easily reconstruct F(x1,..., xn). In this paper, we prove that among all duplication-free representations, the most computationally efficient one is a representation in which marginals are supplements by a copula. This result explains why copulas have been successfully used in many applications of statistics: since the copula representation is, in some reasonable sense, the most computationally efficient way of representing multi-D probability distributions.en_US
dc.subjectComputer Scienceen_US
dc.titleWhy copulas have been successful in many practical applications: A theoretical explanation based on computational efficiencyen_US
dc.typeBook Seriesen_US
article.title.sourcetitleLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)en_US
article.volume9376en_US of Texas at El Pasoen_US Mexico State University Las Crucesen_US Mai Universityen_US
Appears in Collections:CMUL: Journal Articles

Files in This Item:
There are no files associated with this item.

Items in CMUIR are protected by copyright, with all rights reserved, unless otherwise indicated.