Asymptotic Approximations For Probability Integrals
Asymptotic Approximations For Probability Integrals Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Asymptotic Approximations For Probability Integrals book. This book definitely worth reading, it is an incredibly well-written.
Asymptotic Approximations for Probability Integrals by Karl W. Breitung Pdf
This book gives a self-contained introduction to the subject of asymptotic approximation for multivariate integrals for both mathematicians and applied scientists. A collection of results of the Laplace methods is given. Such methods are useful for example in reliability, statistics, theoretical physics and information theory. An important special case is the approximation of multidimensional normal integrals. Here the relation between the differential geometry of the boundary of the integration domain and the asymptotic probability content is derived. One of the most important applications of these methods is in structural reliability. Engineers working in this field will find here a complete outline of asymptotic approximation methods for failure probability integrals.
Asymptotic Approximations for Probability Integrals by Karl Wilhelm Breitung Pdf
This book gives a self-contained introduction to the subject of asymptotic approximation for multivariate integrals for both mathematicians and applied scientists. A collection of results of the Laplace methods is given. Such methods are useful for example in reliability, statistics, theoretical physics and information theory. An important special case is the approximation of multidimensional normal integrals. Here the relation between the differential geometry of the boundary of the integration domain and the asymptotic probability content is derived. One of the most important applications of these methods is in structural reliability. Engineers working in this field will find here a complete outline of asymptotic approximation methods for failure probability integrals.
Asymptotic Approximations of Integrals by R. Wong Pdf
Asymptotic Approximations of Integrals deals with the methods used in the asymptotic approximation of integrals. Topics covered range from logarithmic singularities and the summability method to the distributional approach and the Mellin transform technique for multiple integrals. Uniform asymptotic expansions via a rational transformation are also discussed, along with double integrals with a curve of stationary points. For completeness, classical methods are examined as well. Comprised of nine chapters, this volume begins with an introduction to the fundamental concepts of asymptotics, followed by a discussion on classical techniques used in the asymptotic evaluation of integrals, including Laplace's method, Mellin transform techniques, and the summability method. Subsequent chapters focus on the elementary theory of distributions; the distributional approach; uniform asymptotic expansions; and integrals which depend on auxiliary parameters in addition to the asymptotic variable. The book concludes by considering double integrals and higher-dimensional integrals. This monograph is intended for graduate students and research workers in mathematics, physics, and engineering.
Asymptotic Methods for Integrals by Nico M Temme Pdf
This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals. The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on. Contents:Basic Methods for IntegralsBasic Methods: Examples for Special FunctionsOther Methods for IntegralsUniform Methods for IntegralsUniform Methods for Laplace-Type IntegralsUniform Examples for Special FunctionsA Class of Cumulative Distribution Functions Readership: Researchers in applied mathematics, engineering, physics, mathematical statistics, probability theory and biology. The introductory parts and examples will be useful for post-graduate students in mathematics. Key Features:The book gives a complete overview of the classical asymptotic methods for integralsThe many examples give insight in the behavior of the well-known special functionsThe detailed explanations on how to obtain the coefficients in the expansions make the results useful for numerical applications, in particular, for computing special functionsThe many results on asymptotic representations of special functions supplement and extend those in the NIST Handbook of Mathematical FunctionsKeywords:Asymptotic Analysis;Approximation of Integrals;Asymptotic Approximations;Asymptotic Expansions;Steepest Descent Methods;Saddle Point Methods;Stationary Phase Method;Special Functions;Numerical Approximation of Special Functions;Cumulative Distribution FunctionsReviews: “The book is a useful contribution to the literature. It contains many asymptotic formulas that can be used by practitioners.” Zentralblatt MATH
Approximating Integrals via Monte Carlo and Deterministic Methods by Michael Evans,Timothy Swartz Pdf
This book is designed to introduce graduate students and researchers to the primary methods useful for approximating integrals. The emphasis is on those methods that have been found to be of practical use, and although the focus is on approximating higher- dimensional integrals the lower-dimensional case is also covered. Included in the book are asymptotic techniques, multiple quadrature and quasi-random techniques as well as a complete development of Monte Carlo algorithms. For the Monte Carlo section importance sampling methods, variance reduction techniques and the primary Markov Chain Monte Carlo algorithms are covered. This book brings these various techniques together for the first time, and hence provides an accessible textbook and reference for researchers in a wide variety of disciplines.
Structural Reliability Analysis and Prediction by Robert E. Melchers,Andre T. Beck Pdf
Structural Reliability Analysis and Prediction, Third Edition is a textbook which addresses the important issue of predicting the safety of structures at the design stage and also the safety of existing, perhaps deteriorating structures. Attention is focused on the development and definition of limit states such as serviceability and ultimate strength, the definition of failure and the various models which might be used to describe strength and loading. This book emphasises concepts and applications, built up from basic principles and avoids undue mathematical rigour. It presents an accessible and unified account of the theory and techniques for the analysis of the reliability of engineering structures using probability theory. This new edition has been updated to cover new developments and applications and a new chapter is included which covers structural optimization in the context of reliability analysis. New examples and end of chapter problems are also now included.
Reliability and Optimization of Structural Systems by Daniel Straub Pdf
This volume contains 28 papers by renowned international experts on the latest advances in structural reliability methods and applications, engineering risk analysis and decision making, new optimization techniques and various applications in civil engineering. Moreover, several contributions focus on the assessment and optimization of existing str
Asymptotic Expansions of Integrals by Norman Bleistein,Richard A. Handelsman Pdf
Coherent, systematic coverage of standard methods: integration by parts, Watson's lemma, LaPlace's method, stationary phase and steepest descents. Also includes Mellin transform method and less elementary aspects of the method of steepest descents. Abundant exercises. 1975 edition.
Probabilistic Methods for Structural Design by Carlos Guedes Soares Pdf
This book contains contributions from various authors on different important topics related with probabilistic methods used for the design of structures. Initially several of the papers were prepared for advanced courses on structural reliability or on probabilistic methods for structural design. These courses have been held in different countries and have been given by different groups of lecturers. They were aimed at engineers and researchers who already had some exposure to structural reliability methods and thus they presented overviews of the work in the various topics. The book includes a selection of those contributions, which can be of support for future courses or for engineers and researchers that want to have an update on specific topics. It is considered a complement to the existing textbooks on structural reliability, which normally ensure the coverage of the basic topics but then are not extensive enough to cover some more specialised aspects. In addition to the contributions drawn from those lectures there are several papers that have been prepared specifically for this book, aiming at complementing the others in providing an overall account of the recent advances in the field. It is with sadness that in the meanwhile we have seen the disappearance of two of the contributors to the book and, in fact two of the early contributors to this field.
Stochastic Programming by Kurt Marti,Peter Kall Pdf
New theoretical insight into several branches of reliability-oriented optimization of stochastic systems, new computational approaches and technical/economic applications of stochastic programming methods can be found in this volume.
Recent Advances in Structural Engineering by Anonim Pdf
This book contains state-of-the-art review articles on specific research areas in the civil engineering discipline-the areas include geotechnical engineering, hydraulics and water resources engineering, and structural engineering. The articles are written by invited authors who are currently active at the international level in their respective research fields.
Reliability and Optimization of Structural Systems ’90 by A. Der Kiureghian,P. Thoft-Christensen Pdf
This proceedings volume contains papers presented at the Third Scientific Meeting of the IFIP Working Group on "Reliabilty and Optimization of Structural Systems". The contributions reflect recent developments in the field of modern structural systems optimization and reliability theory and point out directions for further research. Also perspectives for the education in this field were discussed.
