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dc.contributor.authorRojo, Javier
dc.date.accessioned 2013-03-19T18:27:29Z
dc.date.available 2013-03-19T18:27:29Z
dc.date.issued 2013
dc.identifier.citation Rojo, Javier. "Heavy-tailed densities." WIREs Computational Statistics, 5, (2013) Wiley: 30-40. http://dx.doi.org/10.1002/wics.1236.
dc.identifier.urihttps://hdl.handle.net/1911/70747
dc.description.abstract The concept of heavy- or long-tailed densities (or distributions) has attracted much well-deserved attention in the literature. A quick search in Google using the keywords long-tailed statistics retrieves almost 12 million items. The concept has become a pillar of the theory of extremes, and through its connection with outlier-prone distributions, long-tailed distributions also play a central role in the theory of robustness. The concept of tail heaviness is by now ubiquitous, appearing in a diverse set of disciplines that includes: economics, communications, atmospheric sciences, climate modeling, social sciences, physics, modeling of complex systems, etc. Nevertheless, the precise meaning of ‘long-’ or ‘heavy tails’ remains somewhat elusive. Thus, in a substantial portion of the early literature, long-tailednessmeant that the underlying distributionwas capable of producing anomalous observations in the sense that they were ‘too far’ from themain body of observations. Implicit in these informal definitions was the notion that any distribution that behaved that way had to do so because its tails were longer than those of the normal distribution. This paper discusses tail orderings and several approaches for the classification of probability distributions according to tail heaviness. It is concluded that an approach based on the limiting behavior of the residual life function, and its corresponding characterizations based on functions of regular variation and asymptotic distribution of extreme spacings, provides the more natural and illuminating concepts of tail behavior.
dc.language.iso eng
dc.publisher Wiley
dc.rights Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
dc.title Heavy-tailed densities
dc.type Journal article
dc.citation.journalTitle WIREs Computational Statistics
dc.subject.keywordextreme value theory
functions of regular variation
spacings
failure rate
quantile function
dc.citation.volumeNumber 5
dc.embargo.terms none
dc.type.dcmi Text
dc.identifier.doihttp://dx.doi.org/10.1002/wics.1236
dc.type.publication publisher version
dc.citation.firstpage 30
dc.citation.lastpage 40


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