Please use this identifier to cite or link to this item: `http://cmuir.cmu.ac.th/jspui/handle/6653943832/54416`
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dc.contributor.authorHung T. Nguyenen_US
dc.contributor.authorSongsak Sriboonchittaen_US
dc.contributor.authorOlga Koshelevaen_US
dc.date.accessioned2018-09-04T10:13:10Z-
dc.date.available2018-09-04T10:13:10Z-
dc.date.issued2015-01-01en_US
dc.identifier.issn03029743en_US
dc.identifier.other2-s2.0-84951019499en_US
dc.identifier.other10.1007/978-3-319-25135-6-12en_US
dc.identifier.urihttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84951019499&origin=inwarden_US
dc.identifier.urihttp://cmuir.cmu.ac.th/jspui/handle/6653943832/54416-
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.subjectMathematicsen_US
dc.titleWhy copulas have been successful in many practical applications: A theoretical explanation based on computational efficiencyen_US
dc.typeConference Proceedingen_US
article.title.sourcetitleLecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science)en_US
article.volume9376en_US
article.stream.affiliationsUniversity of Texas at El Pasoen_US
article.stream.affiliationsNew Mexico State University Las Crucesen_US
article.stream.affiliationsChiang Mai Universityen_US
Appears in Collections:CMUL: Journal Articles

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