The Multivariate Normal Distribution
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The Multivariate Normal Distribution
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Author : Y.L. Tong
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Multivariate Normal Distribution written by Y.L. Tong and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
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
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Author : Thu Pham-gia
language : en
Publisher: World Scientific
Release Date : 2021-05-05
Multivariate Normal Distribution The Theory And Applications written by Thu Pham-gia and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-05 with Business & Economics categories.
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
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Author : Heidi H. Andersen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Linear And Graphical Models written by Heidi H. Andersen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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
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Author : Alan Genz
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-09
Computation Of Multivariate Normal And T Probabilities written by Alan Genz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-09 with Computers categories.
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.
The Multivariate Normal Distribution
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Author : Yung Liang Tong
language : en
Publisher:
Release Date : 1992
The Multivariate Normal Distribution written by Yung Liang Tong and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Distribution (Probability theory) categories.
Gaussian Processes For Machine Learning
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Author : Carl Edward Rasmussen
language : en
Publisher: MIT Press
Release Date : 2005-11-23
Gaussian Processes For Machine Learning written by Carl Edward Rasmussen and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-23 with Computers categories.
A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.
The Normal Distribution
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Author : Wlodzimierz Bryc
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Normal Distribution written by Wlodzimierz Bryc and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
A First Course In Multivariate Statistics
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Author : Bernhard Flury
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-08-15
A First Course In Multivariate Statistics written by Bernhard Flury and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-15 with Mathematics categories.
A comprehensive and self-contained introduction to the field, carefully balancing mathematical theory and practical applications. It starts at an elementary level, developing concepts of multivariate distributions from first principles. After a chapter on the multivariate normal distribution reviewing the classical parametric theory, methods of estimation are explored using the plug-in principles as well as maximum likelihood. Two chapters on discrimination and classification, including logistic regression, form the core of the book, followed by methods of testing hypotheses developed from heuristic principles, likelihood ratio tests and permutation tests. Finally, the powerful self-consistency principle is used to introduce principal components as a method of approximation, rounded off by a chapter on finite mixture analysis.
Handbook Of The Normal Distribution
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Author : Jagdish K. Patel
language : en
Publisher:
Release Date : 1982
Handbook Of The Normal Distribution written by Jagdish K. Patel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
A collection of results relating to the normal distribution, tracing the historical development of normal law and providing a compendium of properties. The revised edition introduces the most current estimation procedures for normally distributed samples for researchers and students in theoretical and applied statistics, including expanded treatments of: bivariate normal distribution, normal integrals, Mills' ratio, asymptotic normality, point estimation, and statistical intervals. Annotation copyright by Book News, Inc., Portland, OR
Aspects Of Multivariate Statistical Theory
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Author : Robb J. Muirhead
language : en
Publisher: John Wiley & Sons
Release Date : 2009-09-25
Aspects Of Multivariate Statistical Theory written by Robb J. Muirhead and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-25 with Mathematics categories.
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.