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" Unimodality of Probability Measures "
by Emile M. J. Bertin, Ioan Cuculescu, Radu Theodorescu.
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BL
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| Record Number
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579155
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b408374
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| Main Entry
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Bertin, Emile M. J.
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| Title & Author
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Unimodality of Probability Measures\ by Emile M. J. Bertin, Ioan Cuculescu, Radu Theodorescu.
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| Publication Statement
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Dordrecht :: Springer Netherlands :: Imprint: Springer,, 1997.
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| Series Statement
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Mathematics and Its Applications ;; 382
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| ISBN
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9789401588089
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: 9789048147694
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| Contents
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1 Prelude -- 2 Khinchin structures -- 3 Concepts of unimodality -- 4 Khinchin's classical unimodality -- 5 Discrete unimodality -- 6 Strong unimodality -- 7 Positivity of functional moments -- Symbol index -- Name index.
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| Abstract
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Labor omnia vincit improbus. VIRGIL, Georgica I, 144-145. In the first part of his Theoria combinationis observationum erroribus min imis obnoxiae, published in 1821, Carl Friedrich Gauss [Gau80, p.10] deduces a Chebyshev-type inequality for a probability density function, when it only has the property that its value always decreases, or at least does l not increase, if the absolute value of x increases . One may therefore conjecture that Gauss is one of the first scientists to use the property of 'single-humpedness' of a probability density function in a meaningful probabilistic context. More than seventy years later, zoologist W.F.R. Weldon was faced with 'double humpedness'. Indeed, discussing peculiarities of a population of Naples crabs, possi bly connected to natural selection, he writes to Karl Pearson (E.S. Pearson [Pea78, p.328]): Out of the mouths of babes and sucklings hath He perfected praise! In the last few evenings I have wrestled with a double humped curve, and have overthrown it. Enclosed is the diagram... If you scoff at this, I shall never forgive you. Not only did Pearson not scoff at this bimodal probability density function, he examined it and succeeded in decomposing it into two 'single-humped curves' in his first statistical memoir (Pearson [Pea94]).
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| Subject
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Mathematics.
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Functional equations.
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Distribution (Probability theory).
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Statistics.
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Cuculescu, Ioan.
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Theodorescu, Radu.
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SpringerLink (Online service)
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