SYSTEM RELIABILITY THEORY MODELS STATISTICAL METHODS AND APPLICATIONS WILEY SERIES IN PROBABILITY AND STATISTICS APPLIED PROBABILITY AND STATISTICS SECTION

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A comprehensive introduction to reliability analysis. The first section provides a thorough but elementary prologue to reliability theory. The latter half comprises more advanced analytical tools including Markov processes, renewal theory, life data analysis, accelerated life testing and Bayesian reliability analysis. Features numerous worked examples. Each chapter concludes with a selection of problems plus additional material on applications.

A timely and applied approach to the newly discovered methods and applications of U-statistics Built on years of collaborative research and academic experience, Modern Applied U-Statistics successfully presents a thorough introduction to the theory of U-statistics using in-depth examples and applications that address contemporary areas of study including biomedical and psychosocial research. Utilizing a "learn by example" approach, this book provides an accessible, yet in-depth, treatment of U-statistics, as well as addresses key concepts in asymptotic theory by integrating translational and cross-disciplinary research. The authors begin with an introduction of the essential and theoretical foundations of U-statistics such as the notion of convergence in probability and distribution, basic convergence results, stochastic Os, inference theory, generalized estimating equations, as well as the definition and asymptotic properties of U-statistics. With an emphasis on nonparametric applications when and where applicable, the authors then build upon this established foundation in order to equip readers with the knowledge needed to understand the modern-day extensions of U-statistics that are explored in subsequent chapters. Additional topical coverage includes: Longitudinal data modeling with missing data Parametric and distribution-free mixed-effect and structural equation models A new multi-response based regression framework for non-parametric statistics such as the product moment correlation, Kendall's tau, and Mann-Whitney-Wilcoxon rank tests A new class of U-statistic-based estimating equations (UBEE) for dependent responses Motivating examples, in-depth illustrations of statistical and model-building concepts, and an extensive discussion of longitudinal study designs strengthen the real-world utility and comprehension of this book. An accompanying Web site features SAS? and S-Plus? program codes, software applications, and additional study data. Modern Applied U-Statistics accommodates second- and third-year students of biostatistics at the graduate level and also serves as an excellent self-study for practitioners in the fields of bioinformatics and psychosocial research.

Author : James H. Stapleton
ISBN : 0470183403
Genre : Mathematics
File Size : 74.86 MB
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This concise, yet thorough, book is enhanced with simulations and graphs to build the intuition of readers Models for Probability and Statistical Inference was written over a five-year period and serves as a comprehensive treatment of the fundamentals of probability and statistical inference. With detailed theoretical coverage found throughout the book, readers acquire the fundamentals needed to advance to more specialized topics, such as sampling, linear models, design of experiments, statistical computing, survival analysis, and bootstrapping. Ideal as a textbook for a two-semester sequence on probability and statistical inference, early chapters provide coverage on probability and include discussions of: discrete models and random variables; discrete distributions including binomial, hypergeometric, geometric, and Poisson; continuous, normal, gamma, and conditional distributions; and limit theory. Since limit theory is usually the most difficult topic for readers to master, the author thoroughly discusses modes of convergence of sequences of random variables, with special attention to convergence in distribution. The second half of the book addresses statistical inference, beginning with a discussion on point estimation and followed by coverage of consistency and confidence intervals. Further areas of exploration include: distributions defined in terms of the multivariate normal, chi-square, t, and F (central and non-central); the one- and two-sample Wilcoxon test, together with methods of estimation based on both; linear models with a linear space-projection approach; and logistic regression. Each section contains a set of problems ranging in difficulty from simple to more complex, and selected answers as well as proofs to almost all statements are provided. An abundant amount of figures in addition to helpful simulations and graphs produced by the statistical package S-Plus(r) are included to help build the intuition of readers.

Author : Kenneth S. Stephens
ISBN : 9780873898317
Genre : Computers
File Size : 23.36 MB
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Many reliability engineers are gainfully employed in considerations of the physical nature of components and systemsbringing to bear theories and methodologies of physics, electronics, mechanics, material science, chemistry, and so on. But when a product has been designed and manufactured, its performance in terms of durability, strength, and life become a matter of test, measurement, and analysis. Statistical theories and methodologies provide a large number of analytical tools to assist the reliability engineer in studying the performance of products and the fruits of the physical considerations, even revealing further improvements that can be made in the physical properties. Hence, reliability is a multidisciplined field of endeavor. Statistical theories and methodologies allow estimation of important characteristics as well as levels of confidence or assurance (or lack thereof) with respect to the estimations. They also provide direction in actions necessary to improve estimates and confidence levels if results are too variable to render important decisions. Some derivations are contained in this text, but the approach here is meant to be more practical, in following each topic introduced and expanded with examples. On each topic covered, reasonably practical examples are used to illustrate and demonstrate the procedures introduced and discussed. For all of these examples either Excel files or Minitab files or both have been prepared, and these files are located on the CD accompanying the text in order to reduce the size of the text, but more importantly so that they can be readily accessed and opened directly in their respective software packages to permit the preparation of new files specifically for use by the reader.

Author : Harry H. Panjer
ISBN : 9780470051306
Genre : Business & Economics
File Size : 30.14 MB
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Discover how to optimize business strategies from both qualitative and quantitative points of view Operational Risk: Modeling Analytics is organized around the principle that the analysis of operational risk consists, in part, of the collection of data and the building of mathematical models to describe risk. This book is designed to provide risk analysts with a framework of the mathematical models and methods used in the measurement and modeling of operational risk in both the banking and insurance sectors. Beginning with a foundation for operational risk modeling and a focus on the modeling process, the book flows logically to discussion of probabilistic tools for operational risk modeling and statistical methods for calibrating models of operational risk. Exercises are included in chapters involving numerical computations for students' practice and reinforcement of concepts. Written by Harry Panjer, one of the foremost authorities in the world on risk modeling and its effects in business management, this is the first comprehensive book dedicated to the quantitative assessment of operational risk using the tools of probability, statistics, and actuarial science. In addition to providing great detail of the many probabilistic and statistical methods used in operational risk, this book features: * Ample exercises to further elucidate the concepts in the text * Definitive coverage of distribution functions and related concepts * Models for the size of losses * Models for frequency of loss * Aggregate loss modeling * Extreme value modeling * Dependency modeling using copulas * Statistical methods in model selection and calibration Assuming no previous expertise in either operational risk terminology or in mathematical statistics, the text is designed for beginning graduate-level courses on risk and operational management or enterprise risk management. This book is also useful as a reference for practitioners in both enterprise risk management and risk and operational management.

The essentials of regression analysis through practical applications Regression analysis is a conceptually simple method for investigating relationships among variables. Carrying out a successful application of regression analysis, however, requires a balance of theoretical results, empirical rules, and subjective judgement. Regression Analysis by Example, Fourth Edition has been expanded and thoroughly updated to reflect recent advances in the field. The emphasis continues to be on exploratory data analysis rather than statistical theory. The book offers in-depth treatment of regression diagnostics, transformation, multicollinearity, logistic regression, and robust regression. This new edition features the following enhancements: Chapter 12, Logistic Regression, is expanded to reflect the increased use of the logit models in statistical analysis A new chapter entitled Further Topics discusses advanced areas of regression analysis Reorganized, expanded, and upgraded exercises appear at the end of each chapter A fully integrated Web page provides data sets Numerous graphical displays highlight the significance of visual appeal Regression Analysis by Example, Fourth Edition is suitable for anyone with an understanding of elementary statistics. Methods of regression analysis are clearly demonstrated, and examples containing the types of irregularities commonly encountered in the real world are provided. Each example isolates one or two techniques and features detailed discussions of the techniques themselves, the required assumptions, and the evaluated success of each technique. The methods described throughout the book can be carried out with most of the currently available statistical software packages, such as the software package R. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Author : David J. Marchette
ISBN : 0471722081
Genre : Mathematics
File Size : 84.66 MB
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A timely convergence of two widely used disciplines Random Graphs for Statistical Pattern Recognition is the firstbook to address the topic of random graphs as it applies tostatistical pattern recognition. Both topics are of vital interestto researchers in various mathematical and statistical fields andhave never before been treated together in one book. The use ofdata random graphs in pattern recognition in clustering andclassification is discussed, and the applications for bothdisciplines are enhanced with new tools for the statistical patternrecognition community. New and interesting applications for randomgraph users are also introduced. This important addition to statistical literaturefeatures: Information that previously has been available only throughscattered journal articles Practical tools and techniques for a wide range of real-worldapplications New perspectives on the relationship between patternrecognition and computational geometry Numerous experimental problems to encourage practicalapplications With its comprehensive coverage of two timely fields, enhancedwith many references and real-world examples, Random Graphs forStatistical Pattern Recognition is a valuable resource forindustry professionals and students alike.

Author : Donald Hedeker
ISBN : 9780470036471
Genre : Mathematics
File Size : 69.57 MB
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Longitudinal data analysis for biomedical and behavioral sciences This innovative book sets forth and describes methods for the analysis of longitudinaldata, emphasizing applications to problems in the biomedical and behavioral sciences. Reflecting the growing importance and use of longitudinal data across many areas of research, the text is designed to help users of statistics better analyze and understand this type of data. Much of the material from the book grew out of a course taught by Dr. Hedeker on longitudinal data analysis. The material is, therefore, thoroughly classroom tested and includes a number of features designed to help readers better understand and apply the material. Statistical procedures featured within the text include: * Repeated measures analysis of variance * Multivariate analysis of variance for repeated measures * Random-effects regression models (RRM) * Covariance-pattern models * Generalized-estimating equations (GEE) models * Generalizations of RRM and GEE for categorical outcomes Practical in their approach, the authors emphasize the applications of the methods, using real-world examples for illustration. Some syntax examples are provided, although the authors do not generally focus on software in this book. Several datasets and computer syntax examples are posted on this title's companion Web site. The authors intend to keep the syntax examples current as new versions of the software programs emerge. This text is designed for both undergraduate and graduate courses in longitudinal data analysis. Instructors can take advantage of overheads and additional course materials available online for adopters. Applied statisticians in biomedicine and the social sciences can also use the book as a convenient reference.

Praise for the Third Edition "...this is an excellent book which could easily be used as acourse text..." —International Statistical Institute The Fourth Edition of Applied LinearRegression provides a thorough update of the basic theoryand methodology of linear regression modeling. Demonstrating thepractical applications of linear regression analysis techniques,the Fourth Edition uses interesting, real-worldexercises and examples. Stressing central concepts such as model building, understandingparameters, assessing fit and reliability, and drawing conclusions,the new edition illustrates how to develop estimation, confidence,and testing procedures primarily through the use of least squaresregression. While maintaining the accessible appeal of eachprevious edition,Applied Linear Regression, FourthEdition features: Graphical methods stressed in the initial exploratory phase,analysis phase, and summarization phase of an analysis In-depth coverage of parameter estimates in both simple andcomplex models, transformations, and regression diagnostics Newly added material on topics including testing, ANOVA, andvariance assumptions Updated methodology, such as bootstrapping, cross-validationbinomial and Poisson regression, and modern model selectionmethods Applied Linear Regression, Fourth Edition is anexcellent textbook for upper-undergraduate and graduate-levelstudents, as well as an appropriate reference guide forpractitioners and applied statisticians in engineering, businessadministration, economics, and the social sciences.