Asymptotic Approximations for Probability Integrals PDF Download

Author: Karl W. Breitung
Publisher: Springer
ISBN: 3540490337
Category : Technology & Engineering
Languages : en
Pages : 157

View

Book Description
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.

Author: Karl Wilhelm Breitung
Publisher: Springer Verlag
ISBN: 9780387586175
Category : Mathematics
Languages : en
Pages : 146

View

Book Description
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.

Author: R. Wong
Publisher: Academic Press
ISBN: 1483220710
Category : Mathematics
Languages : en
Pages : 561

View

Book Description
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.

Author: Nico M. Temme
Publisher: World Scientific Publishing Company
ISBN: 9789814612159
Category : Differential equations
Languages : en
Pages : 0

View

Book Description
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.

Author: P. Thoft-Christensen
Publisher: Springer Science & Business Media
ISBN: 3642838286
Category : Technology & Engineering
Languages : en
Pages : 432

View

Book Description
The present book contains 30 papers presented at the 2nd Working Conference on Reliability and Optimization of Structural Systems. The purpose of the Working Group was - to promote modern structural system optimization and reliability theory, - to advance international cooperation in the field of structural system optimization and reliability theory, - to stimulate research, development and application of structural system optimization and reliability theory, - to further the dissemination and exchange of information on reliability and optimization of structural system optimization and reliability theory, - to encourage education in structural system optimization and reliability theory.

Author: Rudiger Rackwitz
Publisher: Springer
ISBN: 0387348662
Category : Computers
Languages : en
Pages : 321

View

Book Description
The 6th meeting sponsored by IFIP Working Group 7.5, on reliability and optimization of structural systems, took place in September 1994 in Assisi, Italy. This book contains the papers presented at the working conference including topics such as reliability of special structures, fatigue, failure modes and time-variant systems relibility.

Author: Zehua Chen
Publisher: CRC Press
ISBN: 0415669863
Category : Mathematics
Languages : en
Pages : 944

View

Book Description
While numerous advanced statistical approaches have recently been developed for quantitative trait loci (QTL) mapping, the methods are scattered throughout the literature. Statistical Methods for QTL Mapping brings together many recent statistical techniques that address the data complexity of QTL mapping. After introducing basic genetics topics and statistical principles, the author discusses the principles of quantitative genetics, general statistical issues of QTL mapping, commonly used one-dimensional QTL mapping approaches, and multiple interval mapping methods. He then explains how to use a feature selection approach to tackle a QTL mapping problem with dense markers. The book also provides comprehensive coverage of Bayesian models and MCMC algorithms and describes methods for multi-trait QTL mapping and eQTL mapping, including meta-trait methods and multivariate sequential procedures. This book emphasizes the modern statistical methodology for QTL mapping as well as the statistical issues that arise during this process. It gives the necessary biological background for statisticians without training in genetics and, likewise, covers statistical thinking and principles for geneticists. Written primarily for geneticists and statisticians specializing in QTL mapping, the book can also be used as a supplement in graduate courses or for self-study by PhD students working on QTL mapping projects.

Author: Alexander Degtyarev
Publisher: Springer Science & Business Media
ISBN: 9783540410881
Category : Mathematics
Languages : en
Pages : 284

View

Book Description
Deformation classes. p. 89.

Author: Emmanuel Farjoun
Publisher: Springer Science & Business Media
ISBN: 9783540606048
Category : Mathematics
Languages : en
Pages : 220

View

Book Description
In this monograph we give an exposition of some recent development in homotopy theory. It relates to advances in periodicity in homotopy localization and in cellular spaces. The notion of homotopy localization is treated quite generally and encompasses all the known idempotent homotopy functors. It is applied to K-theory localizations, to Morava-theories, to Hopkins-Smith theory of types. The method of homotopy colimits is used heavily. It is written with an advanced graduate student in topology and research homotopy theorist in mind.

Author: Robby Caspeele
Publisher: Springer
ISBN: 3319478869
Category : Technology & Engineering
Languages : en
Pages : 526

View

Book Description
This book presents the proceedings of the 14th International Probabilistic Workshop that was held in Ghent, Belgium in December 2016. Probabilistic methods are currently of crucial importance for research and developments in the field of engineering, which face challenges presented by new materials and technologies and rapidly changing societal needs and values. Contemporary needs related to, for example, performance-based design, service-life design, life-cycle analysis, product optimization, assessment of existing structures and structural robustness give rise to new developments as well as accurate and practically applicable probabilistic and statistical engineering methods to support these developments. These proceedings are a valuable resource for anyone interested in contemporary developments in the field of probabilistic engineering applications.