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Author: Gail F. Burrill
Publisher:
ISBN: 9781572322554
Category : Algebra
Languages : en
Pages : 0
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Book Description
Author: Gail F. Burrill
Publisher:
ISBN: 9781572322554
Category : Algebra
Languages : en
Pages : 0
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Book Description
Author: Stefan Trueck
Publisher: Academic Press
ISBN: 0080920306
Category : Business & Economics
Languages : en
Pages : 279
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Book Description
In the last decade rating-based models have become very popular in credit risk management. These systems use the rating of a company as the decisive variable to evaluate the default risk of a bond or loan. The popularity is due to the straightforwardness of the approach, and to the upcoming new capital accord (Basel II), which allows banks to base their capital requirements on internal as well as external rating systems. Because of this, sophisticated credit risk models are being developed or demanded by banks to assess the risk of their credit portfolio better by recognizing the different underlying sources of risk. As a consequence, not only default probabilities for certain rating categories but also the probabilities of moving from one rating state to another are important issues in such models for risk management and pricing. It is widely accepted that rating migrations and default probabilities show significant variations through time due to macroeconomics conditions or the business cycle. These changes in migration behavior may have a substantial impact on the value-at-risk (VAR) of a credit portfolio or the prices of credit derivatives such as collateralized debt obligations (D+CDOs). In Rating Based Modeling of Credit Risk the authors develop a much more sophisticated analysis of migration behavior. Their contribution of more sophisticated techniques to measure and forecast changes in migration behavior as well as determining adequate estimators for transition matrices is a major contribution to rating based credit modeling. Internal ratings-based systems are widely used in banks to calculate their value-at-risk (VAR) in order to determine their capital requirements for loan and bond portfolios under Basel II One aspect of these ratings systems is credit migrations, addressed in a systematic and comprehensive way for the first time in this book The book is based on in-depth work by Trueck and Rachev
Author: David A. Harville
Publisher: CRC Press
ISBN: 1000983757
Category : Mathematics
Languages : en
Pages : 242
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Book Description
• Exercises and solutions are included throughout, from both the first and second volume • Includes coverage of additional topics not covered in the first volume • Highly valuable as a reference book for graduate students or researchers
Author: G. Latouche
Publisher: SIAM
ISBN: 0898714257
Category : Mathematics
Languages : en
Pages : 331
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Book Description
Presents the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner.
Author: Jonathon D. Brown
Publisher: Springer
ISBN: 3319117343
Category : Social Science
Languages : en
Pages : 548
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Book Description
This textbook is an approachable introduction to statistical analysis using matrix algebra. Prior knowledge of matrix algebra is not necessary. Advanced topics are easy to follow through analyses that were performed on an open-source spreadsheet using a few built-in functions. These topics include ordinary linear regression, as well as maximum likelihood estimation, matrix decompositions, nonparametric smoothers and penalized cubic splines. Each data set (1) contains a limited number of observations to encourage readers to do the calculations themselves, and (2) tells a coherent story based on statistical significance and confidence intervals. In this way, students will learn how the numbers were generated and how they can be used to make cogent arguments about everyday matters. This textbook is designed for use in upper level undergraduate courses or first year graduate courses. The first chapter introduces students to linear equations, then covers matrix algebra, focusing on three essential operations: sum of squares, the determinant, and the inverse. These operations are explained in everyday language, and their calculations are demonstrated using concrete examples. The remaining chapters build on these operations, progressing from simple linear regression to mediational models with bootstrapped standard errors.
Author: William H. K. Lam
Publisher: Elsevier
ISBN: 9780080442068
Category : Political Science
Languages : en
Pages : 362
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Book Description
From the contents: Initial planning for urban transit systems (S.C. Wirasinghe). - Public transport timetabling and vehicle scheduling (A. Ceder). - Designing public transport network and routes (A. Ceder). - Transit path choice and assignment model approaches (A. Nuzzolo). - Schedule-based transit assignment models (A. Nuzzolo). - Frequency based transit route choice models (M. Florian).
Author: Tõnu Kollo
Publisher: Springer Science & Business Media
ISBN: 1402034199
Category : Mathematics
Languages : en
Pages : 503
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Book Description
The book presents important tools and techniques for treating problems in m- ern multivariate statistics in a systematic way. The ambition is to indicate new directions as well as to present the classical part of multivariate statistical analysis in this framework. The book has been written for graduate students and statis- cians who are not afraid of matrix formalism. The goal is to provide them with a powerful toolkit for their research and to give necessary background and deeper knowledge for further studies in di?erent areas of multivariate statistics. It can also be useful for researchers in applied mathematics and for people working on data analysis and data mining who can ?nd useful methods and ideas for solving their problems. Ithasbeendesignedasatextbookforatwosemestergraduatecourseonmultiva- ate statistics. Such a course has been held at the Swedish Agricultural University in 2001/02. On the other hand, it can be used as material for series of shorter courses. In fact, Chapters 1 and 2 have been used for a graduate course ”Matrices in Statistics” at University of Tartu for the last few years, and Chapters 2 and 3 formed the material for the graduate course ”Multivariate Asymptotic Statistics” in spring 2002. An advanced course ”Multivariate Linear Models” may be based on Chapter 4. A lot of literature is available on multivariate statistical analysis written for di?- ent purposes and for people with di?erent interests, background and knowledge.
Author: Marvin H. J. Gruber
Publisher: John Wiley & Sons
ISBN: 1118592557
Category : Mathematics
Languages : en
Pages : 391
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Book Description
A self-contained introduction to matrix analysis theory and applications in the field of statistics Comprehensive in scope, Matrix Algebra for Linear Models offers a succinct summary of matrix theory and its related applications to statistics, especially linear models. The book provides a unified presentation of the mathematical properties and statistical applications of matrices in order to define and manipulate data. Written for theoretical and applied statisticians, the book utilizes multiple numerical examples to illustrate key ideas, methods, and techniques crucial to understanding matrix algebra’s application in linear models. Matrix Algebra for Linear Models expertly balances concepts and methods allowing for a side-by-side presentation of matrix theory and its linear model applications. Including concise summaries on each topic, the book also features: Methods of deriving results from the properties of eigenvalues and the singular value decomposition Solutions to matrix optimization problems for obtaining more efficient biased estimators for parameters in linear regression models A section on the generalized singular value decomposition Multiple chapter exercises with selected answers to enhance understanding of the presented material Matrix Algebra for Linear Models is an ideal textbook for advanced undergraduate and graduate-level courses on statistics, matrices, and linear algebra. The book is also an excellent reference for statisticians, engineers, economists, and readers interested in the linear statistical model.
Author: Michael Mortenson
Publisher: Industrial Press
ISBN: 9780831136550
Category : Technology & Engineering
Languages : en
Pages : 350
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Book Description
Author: Feng Fu
Publisher: John Wiley & Sons
ISBN: 1118825438
Category : Technology & Engineering
Languages : en
Pages : 292
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Book Description
The successful design and construction of iconic new buildings relies on a range of advanced technologies, in particular on advanced modelling techniques. In response to the increasingly complex buildings demanded by clients and architects, structural engineers have developed a range of sophisticated modelling software to carry out the necessary structural analysis and design work. Advanced Modelling Techniques in Structural Design introduces numerical analysis methods to both students and design practitioners. It illustrates the modelling techniques used to solve structural design problems, covering most of the issues that an engineer might face, including lateral stability design of tall buildings; earthquake; progressive collapse; fire, blast and vibration analysis; non-linear geometric analysis and buckling analysis . Resolution of these design problems are demonstrated using a range of prestigious projects around the world, including the Buji Khalifa; Willis Towers; Taipei 101; the Gherkin; Millennium Bridge; Millau viaduct and the Forth Bridge, illustrating the practical steps required to begin a modelling exercise and showing how to select appropriate software tools to address specific design problems.
