Unimodality of Probability Measures
By: by Emile M. J. Bertin, Ioan Cuculescu, Radu Theodorescu
Contributors: Cuculescu, Ioan; Theodorescu, Radu
Series: Mathematics and Its Applications -- 382; Mathematics and Its Applications -- 382
Publisher: Springer Netherlands
Published: 1997
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] /
Number of pages: 255
ISBN-13: 9789048147694; 9789401588089
Subjects: Mathematics; Functional equations; Statistics; Distribution (Probability theory)
Description: 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. Chapter 1 lays a foundation for the mathematical reasoning in the chapters following. Chapter 2 deals with the concept of Khinchin space, which leads to the introduction of beta-unimodality in Chapter 3. A discussion on several existing multivariate notions of unimodality concludes this chapter. Chapter 4 concerns Khinchin's classical unimodality, and Chapter 5 is devoted to discrete unimodality. Chapters 6 and 7 treat the concept of strong unimodality on R and to Ibragimov-type results characterising the probability measures which preserve unimodality by convolution, and the concept of slantedness, respectively. Most chapters end with comments, referring to historical aspects or supplying complementary information and open questions. A practical bibliography, as well as symbol, name and subject indices ensure efficient use of this volume. 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.
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