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Author: Kai-Tang Fang
Publisher: Springer
ISBN: 9781489929389
Category : Mathematics
Languages : en
Pages : 220
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Book Description
This book represents the joint effort of three authors, located thousands of miles apart from one another, and its preparation was greatly facilitated by modern communication technology. lt may serve as an additional example of international co-operation among statisticians specializing in statistical distribution theory. In essence we have attempted to amass and digest widely scattered information on multivariate symmetric distributions which has appeared in the Iiterature during the last two decades. Introductory remarks at the beginning of each chapter summarize its content and clarify the importance and applicability of the distributions discussed in these chapters; it seems unnecessary, therefore, to dwell in this Preface on the content of the volume. It should be noted that this work was initiated by the first author, who provided continuous impetus to the project, and a great many of tbe results presented in tbe book stem from bis own researcb or tbe research of bis associates and students during the last 15 years.
Author: Kai-Tang Fang
Publisher: Springer
ISBN: 9781489929389
Category : Mathematics
Languages : en
Pages : 220
Get Book
Book Description
This book represents the joint effort of three authors, located thousands of miles apart from one another, and its preparation was greatly facilitated by modern communication technology. lt may serve as an additional example of international co-operation among statisticians specializing in statistical distribution theory. In essence we have attempted to amass and digest widely scattered information on multivariate symmetric distributions which has appeared in the Iiterature during the last two decades. Introductory remarks at the beginning of each chapter summarize its content and clarify the importance and applicability of the distributions discussed in these chapters; it seems unnecessary, therefore, to dwell in this Preface on the content of the volume. It should be noted that this work was initiated by the first author, who provided continuous impetus to the project, and a great many of tbe results presented in tbe book stem from bis own researcb or tbe research of bis associates and students during the last 15 years.
Author: Kai Wang Fang
Publisher: CRC Press
ISBN: 1351085492
Category : Mathematics
Languages : en
Pages : 230
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Book Description
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.
Author: Theodore Wilbur Anderson
Publisher: IMS
ISBN: 9780940600355
Category : Multivariate analysis
Languages : en
Pages : 502
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Book Description
Author: Jianqing Fan
Publisher: Springer Nature
ISBN: 3030461610
Category : Mathematics
Languages : en
Pages : 384
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Book Description
The collection and analysis of data play an important role in many fields of science and technology, such as computational biology, quantitative finance, information engineering, machine learning, neuroscience, medicine, and the social sciences. Especially in the era of big data, researchers can easily collect data characterised by massive dimensions and complexity. In celebration of Professor Kai-Tai Fang’s 80th birthday, we present this book, which furthers new and exciting developments in modern statistical theories, methods and applications. The book features four review papers on Professor Fang’s numerous contributions to the fields of experimental design, multivariate analysis, data mining and education. It also contains twenty research articles contributed by prominent and active figures in their fields. The articles cover a wide range of important topics such as experimental design, multivariate analysis, data mining, hypothesis testing and statistical models.
Author: Alexandra Dias
Publisher: Routledge
ISBN: 1317976908
Category : Business & Economics
Languages : en
Pages : 310
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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.
Author: Samuel Kotz
Publisher: John Wiley & Sons
ISBN: 0471654035
Category : Mathematics
Languages : en
Pages : 752
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Book Description
Continuous Multivariate Distributions, Volume 1, Second Edition provides a remarkably comprehensive, self-contained resource for this critical statistical area. It covers all significant advances that have occurred in the field over the past quarter century in the theory, methodology, inferential procedures, computational and simulational aspects, and applications of continuous multivariate distributions. In-depth coverage includes MV systems of distributions, MV normal, MV exponential, MV extreme value, MV beta, MV gamma, MV logistic, MV Liouville, and MV Pareto distributions, as well as MV natural exponential families, which have grown immensely since the 1970s. Each distribution is presented in its own chapter along with descriptions of real-world applications gleaned from the current literature on continuous multivariate distributions and their applications.
Author: Y. L. Tong
Publisher: Academic Press
ISBN: 1483269213
Category : Mathematics
Languages : en
Pages : 255
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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: Emilio Gómez Déniz
Publisher: MDPI
ISBN: 3039366467
Category : Social Science
Languages : en
Pages : 146
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Book Description
In recent years, the advances and abilities of computer software have substantially increased the number of scientific publications that seek to introduce new probabilistic modelling frameworks, including continuous and discrete approaches, and univariate and multivariate models. Many of these theoretical and applied statistical works are related to distributions that try to break the symmetry of the normal distribution and other similar symmetric models, mainly using Azzalini's scheme. This strategy uses a symmetric distribution as a baseline case, then an extra parameter is added to the parent model to control the skewness of the new family of probability distributions. The most widespread and popular model is the one based on the normal distribution that produces the skewed normal distribution. In this Special Issue on symmetric and asymmetric distributions, works related to this topic are presented, as well as theoretical and applied proposals that have connections with and implications for this topic. Immediate applications of this line of work include different scenarios such as economics, environmental sciences, biometrics, engineering, health, etc. This Special Issue comprises nine works that follow this methodology derived using a simple process while retaining the rigor that the subject deserves. Readers of this Issue will surely find future lines of work that will enable them to achieve fruitful research results.
Author: Samuel Kotz
Publisher: Springer Science & Business Media
ISBN: 146120173X
Category : Mathematics
Languages : en
Pages : 358
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Book Description
This book describes the inferential and modeling advantages that this distribution, together with its generalizations and modifications, offers. The exposition systematically unfolds with many examples, tables, illustrations, and exercises. A comprehensive index and extensive bibliography also make this book an ideal text for a senior undergraduate and graduate seminar on statistical distributions, or for a short half-term academic course in statistics, applied probability, and finance.
Author: Katarzyna Filipiak
Publisher: Springer Nature
ISBN: 3030754944
Category : Mathematics
Languages : en
Pages : 357
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Book Description
This book presents the latest findings on statistical inference in multivariate, multilinear and mixed linear models, providing a holistic presentation of the subject. It contains pioneering and carefully selected review contributions by experts in the field and guides the reader through topics related to estimation and testing of multivariate and mixed linear model parameters. Starting with the theory of multivariate distributions, covering identification and testing of covariance structures and means under various multivariate models, it goes on to discuss estimation in mixed linear models and their transformations. The results presented originate from the work of the research group Multivariate and Mixed Linear Models and their meetings held at the Mathematical Research and Conference Center in Będlewo, Poland, over the last 10 years. Featuring an extensive bibliography of related publications, the book is intended for PhD students and researchers in modern statistical science who are interested in multivariate and mixed linear models.
