The Normal Distribution: Characterizations with Applications: 100 (Lecture Notes in Statistics, 100) - Softcover

Bryc, Wlodzimierz

 
9780387979908: The Normal Distribution: Characterizations with Applications: 100 (Lecture Notes in Statistics, 100)
Softcover
ISBN 10: 0387979905 ISBN 13: 9780387979908
Verlag: Springer New York, 1995

Inhaltsangabe

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 rel­ 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 intrin­ 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.

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Críticas

"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

Reseña del editor

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 rel­ 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 intrin­ 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.

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Verlag
Springer New York
Erscheinungsdatum
1995
Sprache
Englisch
ISBN 10 
0387979905
ISBN 13 
9780387979908
Einband
Tapa blanda
Anzahl der Seiten
152
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
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Hamburg
Deutschland

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