Symmetric Multivariate And Related Distributions

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.

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.

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.

Significantly revised and expanded, Multivariate Statistical Analysis, Second Edition addresses several added topics related to the properties and characterization of symmetric distributions, elliptically symmetric multivariate distributions, singular symmetric distributions, estimation of covariance matrices, tests of mean against one-sided alternatives, and correlations in symmetrical distributions. Its discussions and examples draw on a wide range of multivariate data, from biometry, agriculture, biomedical science, economics, to filtering and stochastic control, stock market data analysis, and random signal processing.

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.

Significantly revised and expanded, Multivariate Statistical Analysis, Second Edition addresses several added topics related to the properties and characterization of symmetric distributions, elliptically symmetric multivariate distributions, singular symmetric distributions, estimation of covariance matrices, tests of mean against one-sided alternatives, and correlations in symmetrical distributions. Its discussions and examples draw on a wide range of multivariate data, from biometry, agriculture, biomedical science, economics, to filtering and stochastic control, stock market data analysis, and random signal processing.