Unimodality of Probability Measures (Mathematics and Its Applications)

Emile M.J. Bertin/ I. Cuculescu/ Radu Theodorescu

ISBN 10: 0792343182 / ISBN 13: 9780792343189

Published by Kluwer Academic Pub, 1997

About this Item

1st edition. 251 pages. 10.00x6.75x1.00 inches. In Stock.

Seller Inventory # x-0792343182

Bibliographic Details

• Title: Unimodality of Probability Measures (Mathematics and Its Applications)
• Publisher: Kluwer Academic Pub
• Publication Date: 1997
• Language: English
• ISBN 10: 0792343182
• ISBN 13: 9780792343189
• Binding: Hardcover
• Condition: Brand New
• Weight: 0.64 kilograms

About this title

Synopsis

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]).

From the Back Cover

The central theme of this monograph is Khinchin-type representation theorems. An abstract framework for unimodality, an example of applied functional analysis, is developed for the introduction of different types of unimodality and the study of their behaviour. Also, several useful consequences or ramifications tied to these notions are provided. Being neither an encyclopaedia, nor a historical overview, this book aims to serve as an understanding of the basic features of unimodality. Audience: Both researchers and applied mathematicians in the field of unimodality will value this monograph, and it may be used in graduate courses or seminars on this subject too.