The Normal Distribution is popular PDF and ePub book, written by Wlodzimierz Bryc in 2012-12-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, The Normal Distribution can be Read Online from any device for your convenience.
The Normal Distribution Book PDF Summary
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.
Detail Book of The Normal Distribution PDF
- Author : Wlodzimierz Bryc
- Release : 06 December 2012
- Publisher : Springer Science & Business Media
- ISBN : 9781461225607
- Genre : Mathematics
- Total Page : 142 pages
- Language : English
- PDF File Size : 10,6 Mb
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