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Lecture Notes in Statistics

The Normal Distribution

Characterizations with Applications

Authors: Bryc, Wlodzimierz

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About this book

This book is a concise presentation of the normal distribution on the real line and its counterparts on more abstract spaces, which we shall call the Gaussian distributions. The material is selected towards presenting characteristic properties, or characterizations, of the normal distribution. There are many such properties and there are numerous relĀ­ evant works in the literature. In this book special attention is given to characterizations generated by the so called Maxwell's Theorem of statistical mechanics, which is stated in the introduction as Theorem 0.0.1. These characterizations are of interest both intrinĀ­ sically, and as techniques that are worth being aware of. The book may also serve as a good introduction to diverse analytic methods of probability theory. We use characteristic functions, tail estimates, and occasionally dive into complex analysis. In the book we also show how the characteristic properties can be used to prove important results about the Gaussian processes and the abstract Gaussian vectors. For instance, in Section 5.4 we present Fernique's beautiful proofs of the zero-one law and of the integrability of abstract Gaussian vectors. The central limit theorem is obtained via characterizations in Section 7.3.

Reviews

"The book sets recent work in context and represents a valuable addition to the standard texts on characterizations." - J.R. Leslie, Macquarie University, Sydney, Australia

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $109.00
price for USA in USD
  • ISBN 978-1-4612-2560-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $139.00
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
The Normal Distribution
Book Subtitle
Characterizations with Applications
Authors
Series Title
Lecture Notes in Statistics
Series Volume
100
Copyright
1995
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York, Inc.
eBook ISBN
978-1-4612-2560-7
DOI
10.1007/978-1-4612-2560-7
Softcover ISBN
978-0-387-97990-8
Series ISSN
0930-0325
Edition Number
1
Number of Pages
VIII, 139
Topics

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