Bonferroni Type Inequalities With Applications

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Bonferroni-type Inequalities with Applications

Janos Galambos,Italo Simonelli
Bonferroni type Inequalities with Applications Book PDF

Author : Janos Galambos,Italo Simonelli
Publisher : Probability and Its Applications
Page : 288 pages
File Size : 48,9 Mb
Release : 1996-08-09
Category : Mathematics
ISBN : UOM:39015038528868

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Bonferroni-type Inequalities with Applications by Janos Galambos,Italo Simonelli Pdf

Bonferroni-Type Inequalities with Applications presents a large variety of extensions of the methods of inclusion and exclusion. Both methods for generating and methods for proof of such inequalities are discussed. The inequalities are utilized for finding classical probability estimates to modern extreme value theory and combinatorial counting to random subset selection. Applications are given in prime number theory, growth of digits in different algorithms, and in statistics such as estimates of confidence levels of simultaneous interval estimation. The prerequisites include the basic concepts of probability theory and familiarity with combinatorial arguments.

Multivariate Bonferroni-Type Inequalities

John Chen
Multivariate Bonferroni Type Inequalities Book PDF

Author : John Chen
Publisher : CRC Press
Page : 302 pages
File Size : 46,8 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.

Multivariate Bonferroni-Type Inequalities

John Chen
Multivariate Bonferroni Type Inequalities Book PDF

Author : John Chen
Publisher : CRC Press
Page : 304 pages
File Size : 52,6 Mb
Release : 2014-07-22
Category : Mathematics
ISBN : 9781466518438

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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 Fréchet 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.

Improved Bonferroni Inequalities via Abstract Tubes

Klaus Dohmen
Improved Bonferroni Inequalities via Abstract Tubes Book PDF

Author : Klaus Dohmen
Publisher : Springer
Page : 122 pages
File Size : 51,9 Mb
Release : 2003-12-10
Category : Mathematics
ISBN : 9783540393993

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Improved Bonferroni Inequalities via Abstract Tubes by Klaus Dohmen Pdf

This introduction to the recent theory of abstract tubes describes the framework for establishing improved inclusion-exclusion identities and Bonferroni inequalities, which are provably at least as sharp as their classical counterparts while involving fewer terms. All necessary definitions from graph theory, lattice theory and topology are provided. The role of closure and kernel operators is emphasized, and examples are provided throughout to demonstrate the applicability of this new theory. Applications are given to system and network reliability, reliability covering problems and chromatic graph theory. Topics also covered include Zeilberger's abstract lace expansion, matroid polynomials and Möbius functions.

Multivariate Bonferroni-Type Inequalities

John Chen
Multivariate Bonferroni Type Inequalities Book PDF

Author : John Chen
Publisher : Unknown
Page : 0 pages
File Size : 55,9 Mb
Release : 2016
Category : Distribution (Probability theory)
ISBN : OCLC:1156475992

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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.

Probability Theory and Applications

J. Galambos,Imre Kátai
Probability Theory and Applications Book PDF

Author : J. Galambos,Imre Kátai
Publisher : Springer Science & Business Media
Page : 359 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401128179

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Probability Theory and Applications by J. Galambos,Imre Kátai Pdf

This volume contains twenty-two original contributions by leading scientists in many important areas of probability theory and its applications. The material also includes significant new results. Together this collection of papers provides a good state-of-the-art survey of current research in the following areas: inequalities; limit theorems; renewal theory and reliability theory; characterizations of distributions; infinite divisibility of polynomials of normal variables; limiting distributions for order statistics; stochastic processes; functional equations in engineering model building; and probabilistic number theory.

Probability and Statistical Models with Applications

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

Author : CH. A. Charalambides,M.V. Koutras,N. Balakrishnan
Publisher : CRC Press
Page : 665 pages
File Size : 48,8 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

Multiple Comparisons, Selection and Applications in Biometry

Fred. M. Hoppe
Multiple Comparisons Selection and Applications in Biometry Book PDF

Author : Fred. M. Hoppe
Publisher : CRC Press
Page : 576 pages
File Size : 50,8 Mb
Release : 2021-10-01
Category : Mathematics
ISBN : 9781000104929

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Multiple Comparisons, Selection and Applications in Biometry by Fred. M. Hoppe Pdf

Aims to provide in-depth descriptions of the latest developments in multiple comparison methods and selection procedures, while emphasizing biometry. This text is published in honour of the 70th birthday of Charles W. Dunnett - a pioneer in statistical methodology.

Advances in Interdisciplinary Applied Discrete Mathematics

Hemanshu Kaul,Henry Martyn Mulder
Advances in Interdisciplinary Applied Discrete Mathematics Book PDF

Author : Hemanshu Kaul,Henry Martyn Mulder
Publisher : World Scientific
Page : 273 pages
File Size : 44,5 Mb
Release : 2010-09-21
Category : Mathematics
ISBN : 9789814299145

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Advances in Interdisciplinary Applied Discrete Mathematics by Hemanshu Kaul,Henry Martyn Mulder Pdf

Focuses on fields such as consensus and voting theory, clustering, location theory, mathematical biology, and optimization that have seen an upsurge of exciting works over the years using discrete models in modern applications. This book discusses advances in the fields, highlighting the approach of cross-fertilization of ideas across disciplines.

Statistical Theory and Applications

H.N. Nagaraja,Pranab K. Sen,Donald F. Morrison
Statistical Theory and Applications Book PDF

Author : H.N. Nagaraja,Pranab K. Sen,Donald F. Morrison
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461239901

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Statistical Theory and Applications by H.N. Nagaraja,Pranab K. Sen,Donald F. Morrison Pdf

Professor Herbert A. David of Iowa State University will be turning 70 on December 19, 1995. He is reaching this milestone in life with a very distinguished career as a statistician, educator and administrator. We are bringing out this volume in his honor to celebrate this occasion and to recognize his contributions to order statistics, biostatistics and design of experiments, among others; and to the statistical profession in general. With great admiration, respect and pleasure we dedicate this festschrift to Professor Herbert A. David, also known as Herb and H.A. among his friends, colleagues and students. When we began this project in Autumn 1993 and contacted potential contributors from the above group, the enthu siasm was phenomenal. The culmination of this collective endeavor is this volume that is being dedicated to him to celebrate his upcoming birthday. Several individuals have contributed in various capacities to the success ful completion of this project. We sincerely thank the authors of the papers appearing here. Without their dedicated work, we would just have this pref ace! Many of them have served as (anonymous) referees as well. In addition, we are thankful to the following colleagues for their time and advice: John Bunge (Cornell), Z. Govindarajulu (Kentucky), John Klein (Medical U.

CRC Concise Encyclopedia of Mathematics

Eric W. Weisstein
CRC Concise Encyclopedia of Mathematics Book PDF

Author : Eric W. Weisstein
Publisher : CRC Press
Page : 3253 pages
File Size : 48,7 Mb
Release : 2002-12-12
Category : Mathematics
ISBN : 9781420035223

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CRC Concise Encyclopedia of Mathematics by Eric W. Weisstein Pdf

Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d

Scan Statistics and Applications

Joseph Glaz,N. Balakrishnan
Scan Statistics and Applications Book PDF

Author : Joseph Glaz,N. Balakrishnan
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461215783

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Scan Statistics and Applications by Joseph Glaz,N. Balakrishnan Pdf

The study of scan statistics and their applications to many different scientific and engineering problems have received considerable attention in the literature recently. In addition to challenging theoretical problems, the area of scan statis tics has also found exciting applications in diverse disciplines such as archaeol ogy, astronomy, epidemiology, geography, material science, molecular biology, reconnaissance, reliability and quality control, sociology, and telecommunica tion. This will be clearly evident when one goes through this volume. In this volume, we have brought together a collection of experts working in this area of research in order to review some of the developments that have taken place over the years and also to present their new works and point out some open problems. With this in mind, we selected authors for this volume with some having theoretical interests and others being primarily concerned with applications of scan statistics. Our sincere hope is that this volume will thus provide a comprehensive survey of all the developments in this area of research and hence will serve as a valuable source as well as reference for theoreticians and applied researchers. Graduate students interested in this area will find this volume to be particularly useful as it points out many open challenging problems that they could pursue. This volume will also be appropriate for teaching a graduate-level special course on this topic.

Eigenvalues, Inequalities, and Ergodic Theory

Mu-Fa Chen
Eigenvalues Inequalities and Ergodic Theory Book PDF

Author : Mu-Fa Chen
Publisher : Springer Science & Business Media
Page : 239 pages
File Size : 41,5 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9781846281235

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Eigenvalues, Inequalities, and Ergodic Theory by Mu-Fa Chen Pdf

The first and only book to make this research available in the West Concise and accessible: proofs and other technical matters are kept to a minimum to help the non-specialist Each chapter is self-contained to make the book easy-to-use

Encyclopedia of Measurement and Statistics

Neil J. Salkind
Encyclopedia of Measurement and Statistics Book PDF

Author : Neil J. Salkind
Publisher : SAGE
Page : 1417 pages
File Size : 51,8 Mb
Release : 2007
Category : Social Science
ISBN : 9781412916110

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Encyclopedia of Measurement and Statistics by Neil J. Salkind Pdf

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Asymptotic Theory of Statistics and Probability

Anirban DasGupta
Asymptotic Theory of Statistics and Probability Book PDF

Author : Anirban DasGupta
Publisher : Springer Science & Business Media
Page : 727 pages
File Size : 55,8 Mb
Release : 2008-02-06
Category : Mathematics
ISBN : 9780387759715

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Asymptotic Theory of Statistics and Probability by Anirban DasGupta Pdf

This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. The book is unique in its detailed coverage of fundamental topics. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. There is no other book in large sample theory that matches this book in coverage, exercises and examples, bibliography, and lucid conceptual discussion of issues and theorems.