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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.

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.

Linear and Graphical Models

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 401/5 ( reviews)

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Book Synopsis Linear and Graphical Models by : Heidi H. Andersen

Download or read book Linear and Graphical Models written by Heidi H. Andersen. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade, graphical models have become increasingly popular as a statistical tool. This book is the first which provides an account of graphical models for multivariate complex normal distributions. Beginning with an introduction to the multivariate complex normal distribution, the authors develop the marginal and conditional distributions of random vectors and matrices. Then they introduce complex MANOVA models and parameter estimation and hypothesis testing for these models. After introducing undirected graphs, they then develop the theory of complex normal graphical models including the maximum likelihood estimation of the concentration matrix and hypothesis testing of conditional independence.

Computation of Multivariate Normal and t Probabilities

2009-07-09 Computers
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Release : 2009-07-09
Genre : Computers
Kind : eBook
Book Rating : 898/5 ( reviews)

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Book Synopsis Computation of Multivariate Normal and t Probabilities by : Alan Genz

Download or read book Computation of Multivariate Normal and t Probabilities written by Alan Genz. This book was released on 2009-07-09. Available in PDF, EPUB and Kindle. Book excerpt: Multivariate normal and t probabilities are needed for statistical inference in many applications. Modern statistical computation packages provide functions for the computation of these probabilities for problems with one or two variables. This book describes recently developed methods for accurate and efficient computation of the required probability values for problems with two or more variables. The book discusses methods for specialized problems as well as methods for general problems. The book includes examples that illustrate the probability computations for a variety of applications.

Aspects of Multivariate Statistical Theory

2009-09-25 Mathematics
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Release : 2009-09-25
Genre : Mathematics
Kind : eBook
Book Rating : 705/5 ( reviews)

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Book Synopsis Aspects of Multivariate Statistical Theory by : Robb J. Muirhead

Download or read book Aspects of Multivariate Statistical Theory written by Robb J. Muirhead. This book was released on 2009-09-25. Available in PDF, EPUB and Kindle. Book excerpt: The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. ". . . the wealth of material on statistics concerning the multivariate normal distribution is quite exceptional. As such it is a very useful source of information for the general statistician and a must for anyone wanting to penetrate deeper into the multivariate field." -Mededelingen van het Wiskundig Genootschap "This book is a comprehensive and clearly written text on multivariate analysis from a theoretical point of view." -The Statistician Aspects of Multivariate Statistical Theory presents a classical mathematical treatment of the techniques, distributions, and inferences based on multivariate normal distribution. Noncentral distribution theory, decision theoretic estimation of the parameters of a multivariate normal distribution, and the uses of spherical and elliptical distributions in multivariate analysis are introduced. Advances in multivariate analysis are discussed, including decision theory and robustness. The book also includes tables of percentage points of many of the standard likelihood statistics used in multivariate statistical procedures. This definitive resource provides in-depth discussion of the multivariate field and serves admirably as both a textbook and reference.

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