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 : 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.

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.

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

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 Inequalities In Multivariate Distributions

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Author : Y. L. Tong
language : en
Publisher: Academic Press
Release Date : 2014-07-10

Probability Inequalities In Multivariate Distributions written by Y. L. Tong and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-10 with Mathematics categories.

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.

Fundamentals Of Probability A First Course

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Author : Anirban DasGupta
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-04-02

Fundamentals Of Probability A First Course written by Anirban DasGupta 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 2010-04-02 with Mathematics categories.

Probability theory is one branch of mathematics that is simultaneously deep and immediately applicable in diverse areas of human endeavor. It is as fundamental as calculus. Calculus explains the external world, and probability theory helps predict a lot of it. In addition, problems in probability theory have an innate appeal, and the answers are often structured and strikingly beautiful. A solid background in probability theory and probability models will become increasingly more useful in the twenty-?rst century, as dif?cult new problems emerge, that will require more sophisticated models and analysis. Thisisa text onthe fundamentalsof thetheoryofprobabilityat anundergraduate or ?rst-year graduate level for students in science, engineering,and economics. The only mathematical background required is knowledge of univariate and multiva- ate calculus and basic linear algebra. The book covers all of the standard topics in basic probability, such as combinatorial probability, discrete and continuous distributions, moment generating functions, fundamental probability inequalities, the central limit theorem, and joint and conditional distributions of discrete and continuous random variables. But it also has some unique features and a forwa- looking feel.

Discrete Time Markov Jump Linear Systems

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Author : O.L.V. Costa
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30

Discrete Time Markov Jump Linear Systems written by O.L.V. Costa 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 2006-03-30 with Mathematics categories.

Safety critical and high-integrity systems, such as industrial plants and economic systems can be subject to abrupt changes - for instance due to component or interconnection failure, and sudden environment changes etc. Combining probability and operator theory, Discrete-Time Markov Jump Linear Systems provides a unified and rigorous treatment of recent results for the control theory of discrete jump linear systems, which are used in these areas of application. The book is designed for experts in linear systems with Markov jump parameters, but is also of interest for specialists in stochastic control since it presents stochastic control problems for which an explicit solution is possible - making the book suitable for course use. From the reviews: "This text is very well written...it may prove valuable to those who work in the area, are at home with its mathematics, and are interested in stability of linear systems, optimal control, and filtering." Journal of the American Statistical Association, December 2005

Probability Models For Dna Sequence Evolution

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Author : Rick Durrett
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Probability Models For Dna Sequence Evolution written by Rick Durrett 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 2013-03-09 with Mathematics categories.

Our basic question is: Given a collection of DNA sequences, what underlying forces are responsible for the observed patterns of variability? To approach this question we introduce and analyze a number of probability models: the Wright-Fisher model, the coalescent, the infinite alleles model, and the infinite sites model. We study the complications that come from nonconstant population size, recombination, population subdivision, and three forms of natural selection: directional selection, balancing selection, and background selection. These theoretical results set the stage for the investigation of various statistical tests to detect departures from "neutral evolution." The final chapter studies the evolution of whole genomes by chromosomal inversions, reciprocal translocations, and genome duplication. Throughout the book, the theory is developed in close connection with data from more than 60 experimental studies from the biology literature that illustrate the use of these results. This book is written for mathematicians and for biologists alike. We assume no previous knowledge of concepts from biology and only a basic knowledge of probability: a one semester undergraduate course and some familiarity with Markov chains and Poisson processes. Rick Durrett received his Ph.D. in operations research from Stanford University in 1976. He taught in the UCLA mathematics department before coming to Cornell in 1985. He is the author of six books and 125 research papers, and is the academic father of more than 30 Ph.D. students. His current interests are the use of probability models in genetics and ecology, and decreasing the mean and variance of his golf.

Limit Theorems For Randomly Stopped Stochastic Processes

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Author : Dmitrii S. Silvestrov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Limit Theorems For Randomly Stopped Stochastic Processes written by Dmitrii S. Silvestrov 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.

Limit theorems for stochastic processes are an important part of probability theory and mathematical statistics and one model that has attracted the attention of many researchers working in the area is that of limit theorems for randomly stopped stochastic processes. This volume is the first to present a state-of-the-art overview of this field, with many of the results published for the first time. It covers the general conditions as well as the basic applications of the theory, and it covers and demystifies the vast, and technically demanding, Russian literature in detail. A survey of the literature and an extended bibliography of works in the area are also provided. The coverage is thorough, streamlined and arranged according to difficulty for use as an upper-level text if required. It is an essential reference for theoretical and applied researchers in the fields of probability and statistics that will contribute to the continuing extensive studies in the area andremain relevant for years to come.