Bonferroni Type Inequalities With Applications
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Bonferroni Type Inequalities With Applications
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Author : Janos Galambos
language : en
Publisher: Probability and Its Applications
Release Date : 1996-08-09
Bonferroni Type Inequalities With Applications written by Janos Galambos and has been published by Probability and Its Applications this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-09 with Mathematics categories.
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
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Author : John Chen
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Multivariate Bonferroni Type Inequalities written by John Chen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
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
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Author : John Chen
language : en
Publisher: CRC Press
Release Date : 2014-07-22
Multivariate Bonferroni Type Inequalities written by John Chen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-22 with Mathematics categories.
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.
Multivariate Bonferroni Type Inequalities
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Author : John Chen
language : en
Publisher:
Release Date : 2016
Multivariate Bonferroni Type Inequalities written by John Chen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Distribution (Probability theory) categories.
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.
Improved Bonferroni Inequalities Via Abstract Tubes
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Author : Klaus Dohmen
language : en
Publisher: Springer
Release Date : 2003-12-10
Improved Bonferroni Inequalities Via Abstract Tubes written by Klaus Dohmen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-10 with Mathematics categories.
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.
Probability Theory And Applications
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Author : J. Galambos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Probability Theory And Applications written by J. Galambos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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
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Author : CH. A. Charalambides
language : en
Publisher: CRC Press
Release Date : 2000-09-21
Probability And Statistical Models With Applications written by CH. A. Charalambides and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-21 with Mathematics categories.
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
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Author : Fred. M. Hoppe
language : en
Publisher: CRC Press
Release Date : 2021-10-01
Multiple Comparisons Selection And Applications In Biometry written by Fred. M. Hoppe and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-01 with Mathematics categories.
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
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Author : Hemanshu Kaul
language : en
Publisher: World Scientific
Release Date : 2010-09-21
Advances In Interdisciplinary Applied Discrete Mathematics written by Hemanshu Kaul and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-21 with Mathematics categories.
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
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Author : H.N. Nagaraja
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Statistical Theory And Applications written by H.N. Nagaraja and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.