 A note on improved variance bounds for certain bounded unimodal distributionsJohn W. Seaman, Dean M. Young and Virgil R. Marco Statistics & Probability Letters, 1986, vol. 4, issue 6, 273-274 Abstract: Gray and Odell have proved that no symmetric continuous unimodal density on the interval [a,b], with modes interior to (a,b), can have variance exceeding (b - a)2/12. Jacobson has derived more general sufficient conditions for the application of this bound and also has shown that no unimodal distribution on [a,b] can have variance larger than (b - a)2/9. Seaman, Odell and Young have presented even more general sufficient conditions for the smaller bound. In this note, we make use of a dispersion ordering to show that the previous conditions for the smaller bound are far too restrictive. Indeed, no continuous unimodal density [latin small letter f with hook] on [a, b], with [latin small letter f with hook](a) [less-than-or-equals, slant]1/(b - a) and [latin small letter f with hook](b) [less-than-or-equals, slant] 1/(b - a), can have variance larger than (b - a)2/12. Keywords: variance; inequality; upper; bounds; dispersion; ordering (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:4:y:1986:i:6:p:273-274 Ordering information: This journal article can be ordered from Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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