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dc.contributor.authorNelson, Kenric P.en_US
dc.contributor.authorKon, Mark A.en_US
dc.contributor.authorUmarov, Sabir R.en_US
dc.date.accessioned2019-11-06T16:53:12Z
dc.date.available2019-11-06T16:53:12Z
dc.date.issued2019-02-01
dc.identifierhttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000452941100025&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=6e74115fe3da270499c3d65c9b17d654
dc.identifier.citationKenric P Nelson, Mark A Kon, Sabir R Umarov. 2019. "Use of the geometric mean as a statistic for the scale of the coupled Gaussian distributions." PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, Volume 515, pp. 248 - 257. https://doi.org/10.1016/j.physa.2018.09.049
dc.identifier.issn0378-4371
dc.identifier.issn1873-2119
dc.identifier.urihttps://hdl.handle.net/2144/38449
dc.description.abstractThe geometric mean is shown to be an appropriate statistic for the scale of a heavy-tailed coupled Gaussian distribution or equivalently the Student’s t distribution. The coupled Gaussian is a member of a family of distributions parameterized by the nonlinear statistical coupling which is the reciprocal of the degree of freedom and is proportional to fluctuations in the inverse scale of the Gaussian. Existing estimators of the scale of the coupled Gaussian have relied on estimates of the full distribution, and they suffer from problems related to outliers in heavy-tailed distributions. In this paper, the scale of a coupled Gaussian is proven to be equal to the product of the generalized mean and the square root of the coupling. From our numerical computations of the scales of coupled Gaussians using the generalized mean of random samples, it is indicated that only samples from a Cauchy distribution (with coupling parameter one) form an unbiased estimate with diminishing variance for large samples. Nevertheless, we also prove that the scale is a function of the geometric mean, the coupling term and a harmonic number. Numerical experiments show that this estimator is unbiased with diminishing variance for large samples for a broad range of coupling values.en_US
dc.format.extent248 - 257en_US
dc.languageEnglish
dc.publisherELSEVIER SCIENCE BVen_US
dc.relation.ispartofPHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
dc.subjectPhysical sciencesen_US
dc.subjectPhysicsen_US
dc.subjectComplex systemsen_US
dc.subjectInformation theoryen_US
dc.subjectNonextensive statistical mechanicsen_US
dc.subjectHeavy-tailen_US
dc.subjectMathematical physicsen_US
dc.subjectQuantum physicsen_US
dc.subjectFluids & plasmasen_US
dc.titleUse of the geometric mean as a statistic for the scale of the coupled Gaussian distributionsen_US
dc.typeArticleen_US
dc.description.versionAccepted manuscripten_US
dc.identifier.doi10.1016/j.physa.2018.09.049
pubs.elements-sourceweb-of-scienceen_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Mathematics & Statisticsen_US
pubs.publication-statusPublisheden_US
dc.identifier.orcid0000-0001-5902-9412 (Kon, Mark A)
dc.identifier.mycv363535


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