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Probability Integrals of Multivariate Normal and Multivariate T

1962 Multivariate analysis
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Release : 1962
Genre : Multivariate analysis
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Probability Integrals of Multivariate Normal and Multivariate T by : S. S. Gupta

Download or read book Probability Integrals of Multivariate Normal and Multivariate T written by S. S. Gupta. This book was released on 1962. Available in PDF, EPUB and Kindle. Book excerpt: This paper gives a survey of the work on multivariate probability integral and related functions starting with the bivariate case and includes the author's recent work on the probability integrals of the multivariate normal and a multivariate analogue of Student's t. An annotated bibliography on evaluation of multivariate normal and t probability integrals (189 entries) is included. (Author).

Computation of Multivariate Normal and t Probabilities

2009-07-09 Computers
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Release : 2009-07-09
Genre : Computers
Kind : eBook
Book Rating : 898/5 ( reviews)

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Book Synopsis Computation of Multivariate Normal and t Probabilities by : Alan Genz

Download or read book Computation of Multivariate Normal and t Probabilities written by Alan Genz. This book was released on 2009-07-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Multivariate T-Distributions and Their Applications

2004-02-16 Mathematics
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Release : 2004-02-16
Genre : Mathematics
Kind : eBook
Book Rating : 549/5 ( reviews)

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Book Synopsis Multivariate T-Distributions and Their Applications by : Samuel Kotz

Download or read book Multivariate T-Distributions and Their Applications written by Samuel Kotz. This book was released on 2004-02-16. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Multivariate Normal Distribution

2012-12-06 Business & Economics
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Release : 2012-12-06
Genre : Business & Economics
Kind : eBook
Book Rating : 557/5 ( reviews)

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Book Synopsis The Multivariate Normal Distribution by : Y.L. Tong

Download or read book The Multivariate Normal Distribution written by Y.L. Tong. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Probability Inequalities in Multivariate Distributions

2014-07-10 Mathematics
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Release : 2014-07-10
Genre : Mathematics
Kind : eBook
Book Rating : 213/5 ( reviews)

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Book Synopsis Probability Inequalities in Multivariate Distributions by : Y. L. Tong

Download or read book Probability Inequalities in Multivariate Distributions written by Y. L. Tong. This book was released on 2014-07-10. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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