Probability Inequalities In Multivariate Distributions

Author : Y. L. Tong
Publisher : Academic Press
Page : 256 pages
File Size : 45,6 Mb
Release : 2014-07-10
Category : Mathematics
ISBN : 9781483269214

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Probability Inequalities in Multivariate Distributions by Y. L. Tong Pdf

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 : Zhengyan Lin,Zhidong Bai
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 55,8 Mb
Release : 2011-05-30
Category : Mathematics
ISBN : 9783642052613

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Probability Inequalities by Zhengyan Lin,Zhidong Bai Pdf

Inequality has become an essential tool in many areas of mathematical research, for example in probability and statistics where it is frequently used in the proofs. "Probability Inequalities" covers inequalities related with events, distribution functions, characteristic functions, moments and random variables (elements) and their sum. The book shall serve as a useful tool and reference for scientists in the areas of probability and statistics, and applied mathematics. Prof. Zhengyan Lin is a fellow of the Institute of Mathematical Statistics and currently a professor at Zhejiang University, Hangzhou, China. He is the prize winner of National Natural Science Award of China in 1997. Prof. Zhidong Bai is a fellow of TWAS and the Institute of Mathematical Statistics; he is a professor at the National University of Singapore and Northeast Normal University, Changchun, China.

Author : Y.L. Tong
Publisher : Springer Science & Business Media
Page : 281 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9781461396550

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The Multivariate Normal Distribution by Y.L. Tong Pdf

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 : Moshe Shaked
Publisher : IMS
Page : 434 pages
File Size : 54,6 Mb
Release : 1992
Category : Mathematics
ISBN : 0940600293

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Stochastic Inequalities by Moshe Shaked Pdf

Author : Karl C. Mosler
Publisher : IMS
Page : 414 pages
File Size : 45,5 Mb
Release : 1991
Category : Education
ISBN : 0940600269

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Stochastic Orders and Decision Under Risk by Karl C. Mosler Pdf

Author : Yung Liang Tong
Publisher : IMS
Page : 270 pages
File Size : 50,5 Mb
Release : 1984
Category : Mathematics
ISBN : 0940600048

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Inequalities in Statistics and Probability by Yung Liang Tong Pdf

Author : Kai Wang Fang
Publisher : CRC Press
Page : 126 pages
File Size : 40,9 Mb
Release : 2018-01-18
Category : Mathematics
ISBN : 9781351093941

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Symmetric Multivariate and Related Distributions by Kai Wang Fang Pdf

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 : CH. A. Charalambides,M.V. Koutras,N. Balakrishnan
Publisher : CRC Press
Page : 665 pages
File Size : 50,9 Mb
Release : 2000-09-21
Category : Mathematics
ISBN : 9781420036084

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Probability and Statistical Models with Applications by CH. A. Charalambides,M.V. Koutras,N. Balakrishnan Pdf

This monograph of carefully collected articles reviews recent developments in theoretical and applied statistical science, highlights current noteworthy results and illustrates their applications; and points out possible new directions to pursue. With its enlightening account of statistical discoveries and its numerous figures and tables, Probabili

Author : Samuel Kotz,N. Balakrishnan,Norman L. Johnson
Publisher : John Wiley & Sons
Page : 752 pages
File Size : 51,6 Mb
Release : 2004-04-05
Category : Mathematics
ISBN : 9780471654032

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Continuous Multivariate Distributions, Volume 1 by Samuel Kotz,N. Balakrishnan,Norman L. Johnson Pdf

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 : Karl Mosler,Marco Scarsini
Publisher : Springer Science & Business Media
Page : 385 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642499722

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Stochastic Orders and Applications by Karl Mosler,Marco Scarsini Pdf

A bibliography on stochastic orderings. Was there a real need for it? In a time of reference databases as the MathSci or the Science Citation Index or the Social Science Citation Index the answer seems to be negative. The reason we think that this bibliog raphy might be of some use stems from the frustration that we, as workers in the field, have often experienced by finding similar results being discovered and proved over and over in different journals of different disciplines with different levels of mathematical so phistication and accuracy and most of the times without cross references. Of course it would be very unfair to blame an economist, say, for not knowing a result in mathematical physics, or vice versa, especially when the problems and the languages are so far apart that it is often difficult to recognize the analogies even after further scrutiny. We hope that collecting the references on this topic, regardless of the area of application, will be of some help, at least to pinpoint the problem. We use the term stochastic ordering in a broad sense to denote any ordering relation on a space of probability measures. Questions that can be related to the idea of stochastic orderings are as old as probability itself. Think for instance of the problem of comparing two gambles in order to decide which one is more favorable.

Author : Kenneth S. Miller
Publisher : Unknown
Page : 186 pages
File Size : 50,6 Mb
Release : 1975
Category : Mathematics
ISBN : UOM:39015038937689

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Multivariate Distributions by Kenneth S. Miller Pdf

Author : Kocherlakota
Publisher : CRC Press
Page : 384 pages
File Size : 55,8 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351463461

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Bivariate Discrete Distributions by Kocherlakota Pdf

This useful reference/text provides a comprehensive study of the various bivariate discretedistributions that have appeared in the literature- written in an accessible manner thatassumes no more than a first course in mathematical statistics.Supplying individualized treatment of topics while simultaneously exploiting the interrelationshipsof the material, Bivariate Discrete Distributions details the latest techniques ofcomputer simulation for the distributions considered ... contains a general introduction tothe structural properties of discrete distributions, including generating functions, momentrelationships, and the basic ideas of generalizing . . . develops distributions using samplingschemes . .. explores the role of compounding ... covers Waring and "short" distributionsfor use in accident theory ... discusses problems of statistical inference, emphasizing techniquespertinent to the discrete case ... and much more!Containing over 1000 helpful equations, Bivariate Discrete Distributions is

Author : John Chen
Publisher : CRC Press
Page : 302 pages
File Size : 49,8 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781466518452

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Multivariate Bonferroni-Type Inequalities by John Chen Pdf

Multivariate Bonferroni-Type Inequalities: Theory and Applications presents a systematic account of research discoveries on multivariate Bonferroni-type inequalities published in the past decade. The emergence of new bounding approaches pushes the conventional definitions of optimal inequalities and demands new insights into linear and Frechet optimality. The book explores these advances in bounding techniques with corresponding innovative applications. It presents the method of linear programming for multivariate bounds, multivariate hybrid bounds, sub-Markovian bounds, and bounds using Hamilton circuits. The first half of the book describes basic concepts and methods in probability inequalities. The author introduces the classification of univariate and multivariate bounds with optimality, discusses multivariate bounds using indicator functions, and explores linear programming for bivariate upper and lower bounds. The second half addresses bounding results and applications of multivariate Bonferroni-type inequalities. The book shows how to construct new multiple testing procedures with probability upper bounds and goes beyond bivariate upper bounds by considering vectorized upper and hybrid bounds. It presents an optimization algorithm for bivariate and multivariate lower bounds and covers vectorized high-dimensional lower bounds with refinements, such as Hamilton-type circuits and sub-Markovian events. The book concludes with applications of probability inequalities in molecular cancer therapy, big data analysis, and more.

Author : Theodore Wilbur Anderson,Ingram Olkin
Publisher : IMS
Page : 502 pages
File Size : 48,5 Mb
Release : 1994
Category : Multivariate analysis
ISBN : 0940600358

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Multivariate Analysis and Its Applications by Theodore Wilbur Anderson,Ingram Olkin Pdf

Author : Samuel Kotz,Saralees Nadarajah
Publisher : Cambridge University Press
Page : 296 pages
File Size : 42,9 Mb
Release : 2004-02-16
Category : Mathematics
ISBN : 0521826543

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Multivariate T-Distributions and Their Applications by Samuel Kotz,Saralees Nadarajah Pdf

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.