
Unimodality of Probability Measures
Kluwer Academic Publishers
Published on 30. November 1996
Book
Hardback
XIV, 256 pages
978-0-7923-4318-9 (ISBN)
Description
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]).
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]).
More details
Series
Edition
1997 ed.
Language
English
Place of publication
Dordrecht
Netherlands
Target group
Professional and scholarly
Research
Illustrations
XIV, 256 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 20 mm
Weight
576 gr
ISBN-13
978-0-7923-4318-9 (9780792343189)
DOI
10.1007/978-94-015-8808-9
Schweitzer Classification
Other editions
Additional editions

Emile M.J. Bertin | I. Cuculescu | Radu Theodorescu
Unimodality of Probability Measures
Book
12/2010
Springer
€160.49
Shipment within 15-20 days
Content
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.