Computation of Multivariate Normal and t Probabilities PDF Download

Author: Alan Genz
Publisher: Springer Science & Business Media
ISBN: 3642016898
Category : Computers
Languages : en
Pages : 130

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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: S. S. Gupta
Publisher:
ISBN:
Category : Multivariate analysis
Languages : en
Pages : 124

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Book Description
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).

Author: Samuel Kotz
Publisher: Cambridge University Press
ISBN: 9780521826549
Category : Mathematics
Languages : en
Pages : 296

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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: Y. L. Tong
Publisher: Academic Press
ISBN: 1483269213
Category : Mathematics
Languages : en
Pages : 256

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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: Y.L. Tong
Publisher: Springer Science & Business Media
ISBN: 1461396557
Category : Business & Economics
Languages : en
Pages : 281

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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: S. Panchapakesan
Publisher: Springer Science & Business Media
ISBN: 1461223083
Category : Mathematics
Languages : en
Pages : 478

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Book Description
Shanti S. Gupta has made pioneering contributions to ranking and selection theory; in particular, to subset selection theory. His list of publications and the numerous citations his publications have received over the last forty years will amply testify to this fact. Besides ranking and selection, his interests include order statistics and reliability theory. The first editor's association with Shanti Gupta goes back to 1965 when he came to Purdue to do his Ph.D. He has the good fortune of being a student, a colleague and a long-standing collaborator of Shanti Gupta. The second editor's association with Shanti Gupta began in 1978 when he started his research in the area of order statistics. During the past twenty years, he has collaborated with Shanti Gupta on several publications. We both feel that our lives have been enriched by our association with him. He has indeed been a friend, philosopher and guide to us.

Author:
Publisher:
ISBN:
Category : Weights and measures
Languages : en
Pages : 574

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Book Description

Author: Brian L. Joiner
Publisher:
ISBN:
Category : Annals of mathematical statistics
Languages : en
Pages : 512

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Book Description
All articles, notes, queries, corrigenda, and obituaries appearing in the following journals during the indicated years are indexed: Annals of mathematical statistics, 1961-1969; Biometrics, 1965-1969#3; Biometrics, 1951-1969; Journal of the American Statistical Association, 1956-1969; Journal of the Royal Statistical Society, Series B, 1954-1969,#2; South African statistical journal, 1967-1969,#2; Technometrics, 1959-1969.--p.iv.

Author: Robert E. Odeh
Publisher: American Mathematical Soc.
ISBN: 9780821819111
Category : Mathematical statistics
Languages : en
Pages : 388

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Book Description

Author: Samuel Kotz
Publisher: World Scientific
ISBN: 9812380574
Category : Technology & Engineering
Languages : en
Pages : 273

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Book Description
This important book presents developments in a remarkable field of inquiry in statistical/probability theory -- the stressstrength model. Many papers in the field include the enigmatic "words" P(XThe StressStrength Model and Its Generalizations collects and digests theoretical and practical results on the theory and applications of the stressstrength relationships in industrial and economic systems -- results that have been scattered in the literature during the last 40-odd years -- and augments and presents them for the first time in a unified manner suitable for practitioners as well as probabilists and theoretical and applied statisticians.