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dc.contributor.authorEl Barmi, Hammou
dc.contributor.authorMukerjee, Hari
dc.date.accessioned2012-06-20T22:07:54Z
dc.date.available2012-06-20T22:07:54Z
dc.date.issued2009-04
dc.identifier.citationElbarmi, H. and H. Mukerjee (2009). "Peakedness and peakedness ordering in symmetric distributions." J. Multivar. Anal. 100(4): 594-603.en_US
dc.identifier.issn0047-259X
dc.identifier.issn1095-7243
dc.identifier.urihttp://hdl.handle.net/10057/5198
dc.identifier.urihttp://dx.doi.org/10.1016/j.jmva.2008.06.011
dc.descriptionClick on the DOI link below to access the article (may not be free).en_US
dc.description.abstractThere are many ways to measure the dispersion of a random variable. One such method uses the concept of peakedness. If the random variable X is symmetric about a point , then Birnbaum [Z.W. Birnbaum, On random variables with comparable peakedness, The Annals of Mathematical Statistics 19 (1948) 76 81] defined the function P .x/ D P.jX 􀀀 j x/; x 0, as the peakedness of X. If two random variables, X and Y, are symmetric about the points and , respectively, then X is said to be less peaked than Y, denoted by X pkd. ; / Y, if P.jX 􀀀 j x/ P.jY 􀀀 j x/ for all x 0, i.e., jX 􀀀 j is stochastically larger than jY 􀀀 j. For normal distributions this is equivalent to variance ordering. Peakedness ordering can be generalized to the case where and are arbitrary points. However, in this paper we study the comparison of dispersions in two continuous random variables, symmetric about their respective medians, using the peakedness concept where normality, and even moment assumptions are not necessary. We provide estimators of the distribution functions under the restriction of symmetry and peakedness ordering, show that they are consistent, derive the weak convergence of the estimators, compare them with the empirical estimators, and provide formulas for statistical inferences. An example is given to illustrate the theoretical results.en_US
dc.language.isoen_USen_US
dc.publisherElsevier Inc.en_US
dc.relation.ispartofseriesJournal of Multivariate Analysis;v.100 no.4
dc.subjectPeakedness
dc.subjectSymmetric distributions
dc.titlePeakedness and peakedness ordering in symmetric distributionsen_US
dc.typeArticleen_US
dc.description.versionPeer reviewed
dc.rights.holderCopyright © 2009, Elsevier


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