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Multivariate Normal Distribution, The: Theory And Applications

2021-05-05 Business & Economics
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Release : 2021-05-05
Genre : Business & Economics
Kind : eBook
Book Rating : 309/5 ( reviews)

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Book Synopsis Multivariate Normal Distribution, The: Theory And Applications by : Thu Pham-gia

Download or read book Multivariate Normal Distribution, The: Theory And Applications written by Thu Pham-gia. This book was released on 2021-05-05. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the reader with user-friendly applications of normal distribution. In several variables it is called the multinormal distribution which is often handled using matrices for convenience. The author seeks to make the arguments less abstract and hence, starts with the univariate case and moves progressively toward the vector and matrix cases. The approach used in the book is a gradual one, going from one scalar variable to a vector variable and to a matrix variable. The author presents the unified aspect of normal distribution, as well as addresses several other issues, including random matrix theory in physics. Other well-known applications, such as Herrnstein and Murray's argument that human intelligence is substantially influenced by both inherited and environmental factors, will be discussed in this book. It is a better predictor of many personal dynamics — including financial income, job performance, birth out of wedlock, and involvement in crime — than are an individual's parental socioeconomic status, or education level, and deserve to be mentioned and discussed.

The Multivariate Normal Distribution

2012-12-06 Business & Economics
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Release : 2012-12-06
Genre : Business & Economics
Kind : eBook
Book Rating : 557/5 ( reviews)

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Book Synopsis The Multivariate Normal Distribution by : Y.L. Tong

Download or read book The Multivariate Normal Distribution written by Y.L. Tong. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: The multivariate normal distribution has played a predominant role in the historical development of statistical theory, and has made its appearance in various areas of applications. Although many of the results concerning the multivariate normal distribution are classical, there are important new results which have been reported recently in the literature but cannot be found in most books on multivariate analysis. These results are often obtained by showing that the multivariate normal density function belongs to certain large families of density functions. Thus, useful properties of such families immedi ately hold for the multivariate normal distribution. This book attempts to provide a comprehensive and coherent treatment of the classical and new results related to the multivariate normal distribution. The material is organized in a unified modern approach, and the main themes are dependence, probability inequalities, and their roles in theory and applica tions. Some general properties of a multivariate normal density function are discussed, and results that follow from these properties are reviewed exten sively. The coverage is, to some extent, a matter of taste and is not intended to be exhaustive, thus more attention is focused on a systematic presentation of results rather than on a complete listing of them.

The Normal Distribution

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 604/5 ( reviews)

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Book Synopsis The Normal Distribution by : Wlodzimierz Bryc

Download or read book The Normal Distribution written by Wlodzimierz Bryc. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Continuous Multivariate Distributions, Volume 1

2019-01-17 Mathematics
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Release : 2019-01-17
Genre : Mathematics
Kind : eBook
Book Rating : 873/5 ( reviews)

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Book Synopsis Continuous Multivariate Distributions, Volume 1 by : Samuel Kotz

Download or read book Continuous Multivariate Distributions, Volume 1 written by Samuel Kotz. This book was released on 2019-01-17. Available in PDF, EPUB and Kindle. Book excerpt: Seit dem Erscheinen der ersten Auflage dieses Werkes (1972) hat sich das Gebiet der kontinuierlichen multivariaten Verteilungen rasch weiterentwickelt. Moderne Anwendungsfelder sind die Erforschung von Hochwasser, Erdbeben, Regenfällen und Stürmen. Entsprechend wurde das Buch überarbeitet und erweitert: Nunmehr zwei Bände beschreiben eine Vielzahl multivariater Verteilungsmodelle anhand zahlreicher Beispiele. (05/00)

Probability Inequalities in Multivariate Distributions

2014-07-10 Mathematics
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Release : 2014-07-10
Genre : Mathematics
Kind : eBook
Book Rating : 213/5 ( reviews)

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Book Synopsis Probability Inequalities in Multivariate Distributions by : Y. L. Tong

Download or read book Probability Inequalities in Multivariate Distributions written by Y. L. Tong. This book was released on 2014-07-10. Available in PDF, EPUB and Kindle. Book excerpt: Probability Inequalities in Multivariate Distributions is a comprehensive treatment of probability inequalities in multivariate distributions, balancing the treatment between theory and applications. The book is concerned only with those inequalities that are of types T1-T5. The conditions for such inequalities range from very specific to very general. Comprised of eight chapters, this volume begins by presenting a classification of probability inequalities, followed by a discussion on inequalities for multivariate normal distribution as well as their dependence on correlation coefficients. The reader is then introduced to inequalities for other well-known distributions, including the multivariate distributions of t, chi-square, and F; inequalities for a class of symmetric unimodal distributions and for a certain class of random variables that are positively dependent by association or by mixture; and inequalities obtainable through the mathematical tool of majorization and weak majorization. The book also describes some distribution-free inequalities before concluding with an overview of their applications in simultaneous confidence regions, hypothesis testing, multiple decision problems, and reliability and life testing. This monograph is intended for mathematicians, statisticians, students, and those who are primarily interested in inequalities.

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