Multivariate T-Distributions and Their Applications PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Multivariate T-Distributions and Their Applications PDF full book. Access full book title Multivariate T-Distributions and Their Applications by Samuel Kotz. Download full books in PDF and EPUB format.
Author: Samuel Kotz
Publisher: Cambridge University Press
ISBN: 9780521826549
Category : Mathematics
Languages : en
Pages : 296
Get Book
Book Description
Almost all the results available in the literature on multivariate t-distributions published in the last 50 years are now collected together in this comprehensive reference. Because these distributions are becoming more prominent in many applications, this book is a must for any serious researcher or consultant working in multivariate analysis and statistical distributions. Much of this material has never before appeared in book form. The first part of the book emphasizes theoretical results of a probabilistic nature. In the second part of the book, these are supplemented by a variety of statistical aspects. Various generalizations and applications are dealt with in the final chapters. The material on estimation and regression models is of special value for practitioners in statistics and economics. A comprehensive bibliography of over 350 references is included.
Author: Samuel Kotz
Publisher: Cambridge University Press
ISBN: 9780521826549
Category : Mathematics
Languages : en
Pages : 296
Get Book
Book Description
Almost all the results available in the literature on multivariate t-distributions published in the last 50 years are now collected together in this comprehensive reference. Because these distributions are becoming more prominent in many applications, this book is a must for any serious researcher or consultant working in multivariate analysis and statistical distributions. Much of this material has never before appeared in book form. The first part of the book emphasizes theoretical results of a probabilistic nature. In the second part of the book, these are supplemented by a variety of statistical aspects. Various generalizations and applications are dealt with in the final chapters. The material on estimation and regression models is of special value for practitioners in statistics and economics. A comprehensive bibliography of over 350 references is included.
Author: Mohammad Ahsanullah
Publisher: Springer Science & Business Media
ISBN: 9462390614
Category : Mathematics
Languages : en
Pages : 157
Get Book
Book Description
The most important properties of normal and Student t-distributions are presented. A number of applications of these properties are demonstrated. New related results dealing with the distributions of the sum, product and ratio of the independent normal and Student distributions are presented. The materials will be useful to the advanced undergraduate and graduate students and practitioners in the various fields of science and engineering.
Author: Y. L. Tong
Publisher: Academic Press
ISBN: 1483269213
Category : Mathematics
Languages : en
Pages : 255
Get Book
Book Description
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.
Author: Alan Genz
Publisher: Springer Science & Business Media
ISBN: 3642016898
Category : Computers
Languages : en
Pages : 126
Get Book
Book Description
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.
Author: Samuel Kotz
Publisher: John Wiley & Sons
ISBN: 0471183873
Category : Mathematics
Languages : en
Pages : 752
Get Book
Book Description
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)
Author: Thu Pham-gia
Publisher: World Scientific
ISBN: 9811235309
Category : Business & Economics
Languages : en
Pages : 494
Get Book
Book Description
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.
Author: Y.L. Tong
Publisher: Springer Science & Business Media
ISBN: 1461396557
Category : Business & Economics
Languages : en
Pages : 281
Get Book
Book Description
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.
Author: Robert L. Mason
Publisher: SIAM
ISBN: 0898714966
Category : Technology & Engineering
Languages : en
Pages : 271
Get Book
Book Description
Detailed coverage of the practical aspects of multivariate statistical process control (MVSPC) based on the application of Hotelling's T2 statistic. MVSPC is the application of multivariate statistical techniques to improve the quality and productivity of an industrial process. Provides valuable insight into the T2 statistic.
Author: Andriëtte Bekker
Publisher: Springer Nature
ISBN: 3031139712
Category : Mathematics
Languages : en
Pages : 434
Get Book
Book Description
Multivariate statistical analysis has undergone a rich and varied evolution during the latter half of the 20th century. Academics and practitioners have produced much literature with diverse interests and with varying multidisciplinary knowledge on different topics within the multivariate domain. Due to multivariate algebra being of sustained interest and being a continuously developing field, its appeal breaches laterally across multiple disciplines to act as a catalyst for contemporary advances, with its core inferential genesis remaining in that of statistics. It is exactly this varied evolution caused by an influx in data production, diffusion, and understanding in scientific fields that has blurred many lines between disciplines. The cross-pollination between statistics and biology, engineering, medical science, computer science, and even art, has accelerated the vast amount of questions that statistical methodology has to answer and report on. These questions are often multivariate in nature, hoping to elucidate uncertainty on more than one aspect at the same time, and it is here where statistical thinking merges mathematical design with real life interpretation for understanding this uncertainty. Statistical advances benefit from these algebraic inventions and expansions in the multivariate paradigm. This contributed volume aims to usher novel research emanating from a multivariate statistical foundation into the spotlight, with particular significance in multidisciplinary settings. The overarching spirit of this volume is to highlight current trends, stimulate a focus on, and connect multidisciplinary dots from and within multivariate statistical analysis. Guided by these thoughts, a collection of research at the forefront of multivariate statistical thinking is presented here which has been authored by globally recognized subject matter experts.
Author: Alexandra Dias
Publisher: Routledge
ISBN: 1317976908
Category : Business & Economics
Languages : en
Pages : 310
Get Book
Book Description
Portfolio theory and much of asset pricing, as well as many empirical applications, depend on the use of multivariate probability distributions to describe asset returns. Traditionally, this has meant the multivariate normal (or Gaussian) distribution. More recently, theoretical and empirical work in financial economics has employed the multivariate Student (and other) distributions which are members of the elliptically symmetric class. There is also a growing body of work which is based on skew-elliptical distributions. These probability models all exhibit the property that the marginal distributions differ only by location and scale parameters or are restrictive in other respects. Very often, such models are not supported by the empirical evidence that the marginal distributions of asset returns can differ markedly. Copula theory is a branch of statistics which provides powerful methods to overcome these shortcomings. This book provides a synthesis of the latest research in the area of copulae as applied to finance and related subjects such as insurance. Multivariate non-Gaussian dependence is a fact of life for many problems in financial econometrics. This book describes the state of the art in tools required to deal with these observed features of financial data. This book was originally published as a special issue of the European Journal of Finance.
