Contributions To Complex Matrix Variate Distributions Theory

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Contributions To Complex Matrix Variate Distributions Theory

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Author : Daya Krishna Nagar
language : en
Publisher: Universidad de Antioquia
Release Date : 2009

Contributions To Complex Matrix Variate Distributions Theory written by Daya Krishna Nagar and has been published by Universidad de Antioquia this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Distribution (Probability theory) categories.

"Random matrices (real or complex) play an important role in the study of multivariate statistical methods. They have been found useful in physics, engineering, economics, psychology and other fields of investigation. Contributions to Complex Matrix Variate Distribution Theory gives a comprehensive coverage of complex random matrices, and defines a number of new complex matrix variate distributions. It also gathers and systematiclly [sic] presents several results on zonal polynomials, invariant polynomials and hypergeometric functions of Hermitian matrices which until now could only be found scattered in various mathematical or statistical journals. This book provides a compact self-contained introduction to the complex matrix variate distribution theory and includes new results that will be a useful source to all those working in the area, stimulate further research, and help advance this field. This book, valuable to researchers, graduate students, and instructors in multivariate statistical analysis, will also interest researchers in a variety of areas including physicists, engineers, psychometricians, and econometricians."--Back cover

Matrix Variate Distributions

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Author : A K Gupta
language : en
Publisher: CRC Press
Release Date : 2018-05-02

Matrix Variate Distributions written by A K Gupta and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-02 with Mathematics categories.

Useful in physics, economics, psychology, and other fields, random matrices play an important role in the study of multivariate statistical methods. Until now, however, most of the material on random matrices could only be found scattered in various statistical journals. Matrix Variate Distributions gathers and systematically presents most of the recent developments in continuous matrix variate distribution theory and includes new results. After a review of the essential background material, the authors investigate the range of matrix variate distributions, including: matrix variate normal distribution Wishart distribution Matrix variate t-distribution Matrix variate beta distribution F-distribution Matrix variate Dirichlet distribution Matrix quadratic forms With its inclusion of new results, Matrix Variate Distributions promises to stimulate further research and help advance the field of multivariate statistical analysis.

Topics In Random Matrix Theory

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Author : Terence Tao
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-03-21

Topics In Random Matrix Theory written by Terence Tao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-21 with Mathematics categories.

The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.

Symmetric Multivariate And Related Distributions

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Author : Kai Wang Fang
language : en
Publisher: CRC Press
Release Date : 2018-01-18

Symmetric Multivariate And Related Distributions written by Kai Wang Fang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-18 with Mathematics categories.

Since the publication of the by now classical Johnson and Kotz Continuous Multivariate Distributions (Wiley, 1972) there have been substantial developments in multivariate distribution theory especially in the area of non-normal symmetric multivariate distributions. The book by Fang, Kotz and Ng summarizes these developments in a manner which is accessible to a reader with only limited background (advanced real-analysis calculus, linear algebra and elementary matrix calculus). Many of the results in this field are due to Kai-Tai Fang and his associates and appeared in Chinese publications only. A thorough literature search was conducted and the book represents the latest work - as of 1988 - in this rapidly developing field of multivariate distributions. The authors are experts in statistical distribution theory.

Kwic Index For Numerical Algebra

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Author : Alston Scott Householder
language : en
Publisher:
Release Date : 1972

Kwic Index For Numerical Algebra written by Alston Scott Householder and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Algebra categories.

An Introduction To Random Matrices

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Author : Greg W. Anderson
language : en
Publisher: Cambridge University Press
Release Date : 2010

An Introduction To Random Matrices written by Greg W. Anderson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.

Introduction To Random Matrices

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Author : Giacomo Livan
language : en
Publisher: Springer
Release Date : 2018-01-16

Introduction To Random Matrices written by Giacomo Livan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-16 with Science categories.

Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a well-organized, readable and user-friendly fashion. This slim and agile book, written in a pedagogical and hands-on style, without sacrificing formal rigor fills this gap. It brings Ph.D. students in Physics, as well as more senior practitioners, through the standard tools and results on random matrices, with an eye on most recent developments that are not usually covered in introductory texts. The focus is mainly on random matrices with real spectrum.The main guiding threads throughout the book are the Gaussian Ensembles. In particular, Wigner’s semicircle law is derived multiple times to illustrate several techniques (e.g., Coulomb gas approach, replica theory).Most chapters are accompanied by Matlab codes (stored in an online repository) to guide readers through the numerical check of most analytical results.

Robust Statistics For Signal Processing

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Author : Abdelhak M. Zoubir
language : en
Publisher: Cambridge University Press
Release Date : 2018-11-08

Robust Statistics For Signal Processing written by Abdelhak M. Zoubir and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-08 with Mathematics categories.

Understand the benefits of robust statistics for signal processing using this unique and authoritative text.

Unicity Of Meromorphic Mappings

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Author : Pei-Chu Hu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18

Unicity Of Meromorphic Mappings written by Pei-Chu Hu 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 2013-04-18 with Mathematics categories.

For a given meromorphic function I(z) and an arbitrary value a, Nevanlinna's value distribution theory, which can be derived from the well known Poisson-Jensen for mula, deals with relationships between the growth of the function and quantitative estimations of the roots of the equation: 1 (z) - a = O. In the 1920s as an application of the celebrated Nevanlinna's value distribution theory of meromorphic functions, R. Nevanlinna [188] himself proved that for two nonconstant meromorphic func tions I, 9 and five distinctive values ai (i = 1,2,3,4,5) in the extended plane, if 1 1- (ai) = g-l(ai) 1M (ignoring multiplicities) for i = 1,2,3,4,5, then 1 = g. Fur 1 thermore, if 1- (ai) = g-l(ai) CM (counting multiplicities) for i = 1,2,3 and 4, then 1 = L(g), where L denotes a suitable Mobius transformation. Then in the 19708, F. Gross and C. C. Yang started to study the similar but more general questions of two functions that share sets of values. For instance, they proved that if 1 and 9 are two nonconstant entire functions and 8 , 82 and 83 are three distinctive finite sets such 1 1 that 1- (8 ) = g-1(8 ) CM for i = 1,2,3, then 1 = g.

A Dynamical Approach To Random Matrix Theory

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Author : László Erdős
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-30

A Dynamical Approach To Random Matrix Theory written by László Erdős and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-30 with Mathematics categories.

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality. This manuscript has been developed and continuously improved over the last five years. The authors have taught this material in several regular graduate courses at Harvard, Munich, and Vienna, in addition to various summer schools and short courses. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.