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Bertin / Theodorescu / Cuculescu

Unimodality of Probability Measures

Medium: Buch
ISBN: 978-90-481-4769-4
Verlag: Springer Netherlands
Erscheinungstermin: 06.12.2010
Lieferfrist: bis zu 10 Tage

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]).


Produkteigenschaften


  • Artikelnummer: 9789048147694
  • Medium: Buch
  • ISBN: 978-90-481-4769-4
  • Verlag: Springer Netherlands
  • Erscheinungstermin: 06.12.2010
  • Sprache(n): Englisch
  • Auflage: 1. Auflage. Softcover version of original hardcover Auflage 1997
  • Serie: Mathematics and Its Applications
  • Produktform: Kartoniert, Previously published in hardcover
  • Gewicht: 417 g
  • Seiten: 256
  • Format (B x H x T): 155 x 235 x 15 mm
  • Ausgabetyp: Kein, Unbekannt
Autoren/Hrsg.

Autoren

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.