Mathematics Books

Book SynopsisOffers coverage of basic and advanced statistical methods, concentrating on graphical inspection, and featuring step-by-step instruction to help non-statisticians understand the methodology.Trade Review"...suitable as a reference book for experienced statisticians, a vehicle for learning the S statistical computing language, or a resource for statistics instructors..." (The American Statistician, Vol. 58, No. 1, February 2004) "...especially useful as an introduction to a wide variety of data analysis techniques." (R News) "...The book is well written - there is an air of common sense throughout - and is at a level which ensures its usefulness for a wide range of readers..." (Zentralblatt Math, Vol. 1001, No.01, 2003) "...the book is a useful and practical introduction to many areas of statistical data analysis." (Computational STatistics & Data Analysis) "...surely not the last statistics book you’ll ever need, but it might well be the first you will ever really use." (Basic Applied Ecology, Vol. 4, No. 3) "...recommended...contains a wealth of sage advice..." (Technometrics, Vol. 45, No. 4, November 2003) “...a practical introduction to statistics...does not cover all...sophisticated statistical and graphical features of the S-Plus system, but provides a first class starting point—and, probably, for most readers, a sufficient end point.” (Quarterly of Applied Mathematics, LXI, No. 4, December 2003) “…a valiant and useful first attempt to present both statistics and S-PLUS together…” (Journal of The Royal Statistical Society Vol.167 No.4) Table of ContentsStatistical methods Introduction to S-Plus Experimental design Central tendency Probability Variance The Normal distribution Power calculations Understanding data: graphical analysis Understanding data: tabular analysis Classical tests Bootstrap and jackknife Statistical models in S-Plus Regression Analysis of variance Analysis of covariance Model criticism Contrasts Split-plot Anova Nested designs and variance components analysis Graphs, functions and transformations Curve fitting and piecewise regression Non-linear regression Multiple regression Model simplification Probability distributions Generalised linear models Proportion data: binomial errors Count data: Poisson errors Binary response variables Tree models Non-parametric smoothing Survival analysis Time series analysis Mixed effects models Spatial statistics Bibliography Index

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Book SynopsisOf related interest. Nonlinear Regression Analysis and its Applications Douglas M. Bates and Donald G. Watts . an extraordinary presentation of concepts and methods concerning the use and analysis of nonlinear regression models. highly recommend[ed].Table of ContentsLinear Regression Analysis. Constructing and Checking the Model. Least Squares Regression. Least Absolute Deviations Regression. M-Regression. Nonparametric Regression. Bayesian Regression. Ridge Regression. Comparisons. Other Methods.

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Book SynopsisThe Schwarz function originates in classical complex analysis and potential theory. Here the author presents the advantages favoring a mode of treatment which unites the subject with modern theory of distributions and partial differential equations thus bridging the gap between two-dimensional geometric and multi-dimensional analysts. Examines the Schwarz function and its relationship to recent investigations regarding inverse problems of Newtonian gravitation, free boundaries, Hele-Shaw flows and the propagation of singularities for holomorphic p.d.e.Table of ContentsThe Schwarz Principle of Reflection. The Logarithmic Potential, Balayage, and Quadrature Domains. Examples of ``Quadrature Identities''. Quadrature Domains: Basic Properties, 1. Quadrature Domains: Basic Properties, 2. Schwarzian Reflection, Revisited. Projectors from L? (dOmega) to H? (dOmega). The Friedrichs Operator. Concluding Remarks. Bibliography. Index.

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Book SynopsisUnique in that it focuses on formulation and case studies rather than solutions procedures covering applications for pure, generalized and integer networks, equivalent formulations plus successful techniques of network models.Table of ContentsNetform Origins and Uses: Why Modeling and Netforms AreImportant. Fundamental Models for Pure Networks. Additional Pure Network Formulation Techniques. Dynamic Network Models. Generalized Networks. Netforms with Discrete Requirements. Appendices. Index.

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Book SynopsisThe most accessible introduction to the theory and practice of multivariate analysis Multivariate Statistical Inference and Applications is a user-friendly introduction to basic multivariate analysis theory and practice for statistics majors as well as nonmajors with little or no background in theoretical statistics. Among the many special features of this extremely accessible first text on multivariate analysis are: * Clear, step-by-step explanations of all key concepts and procedures along with original, easy-to-follow proofs * Numerous problems, examples, and tables of distributions * Many real-world data sets drawn from a wide range of disciplines * Reviews of univariate procedures that give rise to multivariate techniques * An extensive survey of the world literature on multivariate analysis * An in-depth review of matrix theory * A disk including all the data sets and SAS command files for all examples and numerical problems found in the book<

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Book SynopsisA practical guide to selection, screening, and multiplecomparisons This book addresses experimenters who have knowledge of classicalexperimental design methodology and expands their repertoire beyondhypothesis testing by providing statistical methods appropriate forselection, screening, and multiple comparisons. It concentrates onthree types of procedures: selection procedures that use theindifference-zone approach, screening procedures using thesubset approach, and multiple comparison procedures involvingnormal means. This is the first book, specifically designed forpractitioners, to bring into focus many developments in the fieldpreviously covered only in university courses. It also presents newresults on the comparison of procedures that have been obtainedspecifically for this volume. This self-contained volume describes methods for designingexperiments when the scientific objective is selection of besttreatments, screening a set of treatments, and multiple compariTable of ContentsThe Rationale of Selection, Screening and MultipleComparisons. Selecting the Best Treatment in a Single-Factor Normal ResponseExperiment Using the Indifference-Zone Approach. Selecting a Subset Containing the Best Treatment in a NormalResponse Experiment. Multiple Comparison Approaches for Normal ResponseExperiments. Problems Involving a Standard or Control Treatment in NormalResponse Experiments. Selection Problems in Two-Factor Normal Response Experiments. Selecting Best Treatments in Single-Factor Bernoulli ResponseExperiments. Selection Problems for Categorical Response Experiments. Appendices. References. Indexes.

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Book SynopsisIts main objective is to examine the application and relevance of Bayes'' theorem to problems that arise in scientific investigation in which inferences must be made regarding parameter values about which little is known a priori. Begins with a discussion of some important general aspects of the Bayesian approach such as the choice of prior distribution, particularly noninformative prior distribution, the problem of nuisance parameters and the role of sufficient statistics, followed by many standard problems concerned with the comparison of location and scale parameters. The main thrust is an investigation of questions with appropriate analysis of mathematical results which are illustrated with numerical examples, providing evidence of the value of the Bayesian approach.Table of ContentsNature of Bayesian Inference. Standard Normal Theory Inference Problems. Bayesian Assessment of Assumptions: Effect of Non-Normality onInferences About a Population Mean with Generalizations. Bayesian Assessment of Assumptions: Comparison of Variances. Random Effect Models. Analysis of Cross Classification Designs. Inference About Means with Information from More than One Source:One-Way Classification and Block Designs. Some Aspects of Multivariate Analysis. Estimation of Common Regression Coefficients. Transformation of Data. Tables. References. Indexes.

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Book SynopsisOriginally published in 1958, this text offers a simple analysis of the principles of experimental design. Emphasis is placed on basic concepts rather than the calculation of technical details. It is possible to use the book in conjunction with a text on statistical analysis.Table of ContentsPreliminaries. Some Key Assumptions. Designs for the Reduction of Error. Use of Supplementary Observations to Reduce Error. Randomization. Basic Ideas About Factorial Experiments. Design of Simple Factorial Experiments. Choice of Number of Observations. Choice of Units, Treatments, and Observations. More About Latin Squares. Incomplete Nonfactorial Designs. Fractional Replication and Confounding. Cross-Over Designs. Some Special Problems. General Bibliography. Appendix. Indexes.

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Book SynopsisWritten for engineering students, this textbook on numerical methods stresses the typical methods that engineers use in daily practice. A chapter on design introduces problems which bring relevance to the use of this tool in engineering situations.Table of ContentsFOUNDATIONS. Systems of Linear Algebraic Equations. Nonlinear Algebraic Equations. DATA ANALYSIS. Statistics and Least-Squares Approximation. Curve Fitting. NUMERICAL CALCULUS. Differentiation and Integration. Ordinary Differential Equations. ADVANCED TOPICS. Matrix Eigenproblems. Introduction to Partial Differential Equations. Design and Optimization. Appendices. References. Bibliography. Answers to Selected Problems. Index.

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Book SynopsisSequential Stochastic Optimization provides mathematicians and applied researchers with a well-developed framework in which stochastic optimization problems can be formulated and solved.Table of ContentsPreliminaries. Sums of Independent Random Variables. Optimal Stopping. Reduction to a Single Dimension. Accessibility and Filtration Structure. Sequential Sampling. Optimal Sequential Control. Multiarmed Bandits. The Markovian Case. Optimal Switching Between Two Random Walks. Bibliography. Indexes.

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Book SynopsisThe classic text, now completely up to date This Second Edition of State Variables for Engineers is completely updated to reflect both the many changes in the field of systems and control and the fact that today''s first-year graduate students are well prepared in the background skills and techniques needed to handle this material. The book begins with an introduction to the basic concepts behind time domain techniques, comparisons between state variable feedback and classical output feedback, and a discussion of the concepts of observability and controllability. The authors stress the importance of studying matrices and linear spaces by offering state variable representations for continuous linear systems in matrix form along with the solution to the resulting linear matrix differential equation. This treatment demonstrates how these basic linear algebra tools are related to the state variable analysis of linear systems. This new edition retains thorough coverage of the eiTrade Review"...a welcome addition to the set of books on this subject." (International Journal of Robust and Linear Controls, Vol. 12, 2002)Table of ContentsTime Domain Techniques. State Variable Representation of Systems. Matrices, Linear Spaces, and Linear Systems. State Variables and Linear Continuous Systems. State Variables and Linear Discrete-Time Systems. Canonical Forms for Representing Linear Systems. Observers and Controllers. Identification and Estimation. Introduction to Stability Theory and Lyapunov's Method. Appendices. Index.

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Book SynopsisThe format of this text allows students to focus on the topics with which they have the most difficulty, and to refresh themselves on those topics which they have already grasped. Each chapter targets problem areas and supplies references for more detailed help.Table of ContentsSome Basic Concepts. The Number System. Monomials and Polynomials. Special Products and Factoring. Fractions. Exponents, Roots, and Radicals. Linear and Fractional Equations and Formulas. Functions and Graphs. Quadratic Equations. Inequalities. Ratio, Proportion, and Variation. Solving Everyday Problems. Appendices. Index.

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Book SynopsisThis volume presents a detailed description of the statistical distributions that are commonly applied to such fields as engineering, business, economics and the behavioural, biological and environmental sciences.Table of ContentsExtreme Value Distributions. Logistic Distribution. Laplace (Double Exponential) Distributions. Beta Distributions. Uniform (Rectangular) Distributions. F-Distributions. t-Distributions. Noncentral x^2 Distributions. Noncentral F-Distributions. Noncentral t-Distributions. Distributions of Correlation Coefficients. Lifetime Distributions and Miscellaneous Orderings. Abbreviations. Indexes.

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Book SynopsisThe definitive reference for statistical distributions Continuous Univariate Distributions, Volume 1 offers comprehensive guidance toward the most commonly used statistical distributions, including normal, lognormal, inverse Gaussian, Pareto, Cauchy, gamma distributions and more. Each distribution includes clear definitions and properties, plus methods of inference, applications, algorithms, characterizations, and reference to other related distributions. Organized for easy navigation and quick reference, this book is an invaluable resource for investors, data analysts, or anyone working with statistical distributions on a regular basis.Table of ContentsContinuous Distributions (General). Normal Distributions. Lognormal Distributions. Inverse Gaussian (Wald) Distributions. Cauchy Distribution. Gamma Distributions. Chi-Square Distributions Including Chi and Rayleigh. Exponential Distributions. Pareto Distributions. Weibull Distributions. Abbreviations. Indexes.

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Book SynopsisA leading pioneer in the field offers practical applications of this innovative science. Peters describes complex concepts in an easy-to-follow manner for the non-mathematician. He uses fractals, rescaled range analysis and nonlinear dynamical models to explain behavior and understand price movements. These are specific tools employed by chaos scientists to map and measure physical and now, economic phenomena.Table of ContentsFRACTAL TIME SERIES. Failure of the Gaussian Hypothesis. A Fractal Market Hypothesis. FRACTAL (R/S) ANALYSIS. Measuring Memory--The Hurst Process and R/S Analysis. Testing R/S Analysis. Finding Cycles: Periodic and Nonperiodic. APPLYING FRACTAL ANALYSIS. Case Study Methodology. Dow Jones Industrials, 1888-1990: An Ideal Data Set. S&P 500 Tick Data, 1989-1992: Problems with Oversampling. Volatility: A Study in Antipersistence. Problems with Undersampling: Gold and U.K. Inflation. Currencies: A True Hurst Process. FRACTAL NOISE. Fractional Noise and R/S Analysis. Fractal Statistics. Applying Fractal Statistics. NOISY CHAOS. Noisy Chaos and R/S Analysis. Fractal Statistics, Noisy Chaos, and the FMH. Understanding Markets. Appendices. Bibliography. Glossary. Index.

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Book SynopsisA complete, self-contained introduction to a powerful and resurging mathematical discipline. Combinatorial Geometry presents and explains with complete proofs some of the most important results and methods of this relatively young mathematical discipline, started by Minkowski, Fejes Toth, Rogers, and Erd???s.Table of ContentsARRANGEMENTS OF CONVEX SETS. Geometry of Numbers. Approximation of a Convex Set by Polygons. Packing and Covering with Congruent Convex Discs. Lattice Packing and Lattice Covering. The Method of Cell Decomposition. Methods of Blichfeldt and Rogers. Efficient Random Arrangements. Circle Packings and Planar Graphs. ARRANGEMENTS OF POINTS AND LINES. Extremal Graph Theory. Repeated Distances in Space. Arrangement of Lines. Applications of the Bounds on Incidences. More on Repeated Distances. Geometric Graphs. Epsilon Nets and Transversals of Hypergraphs. Geometric Discrepancy. Hints to Exercises. Bibliography. Indexes.

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Book SynopsisPresents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions.Table of ContentsDiscrete Fourier Analysis. Cauchy Integrals. Potential Theory in the Plane. Construction of Conformal Maps: Simply Connected Regions. Construction of Conformal Maps for Multiply ConnectedRegions. Polynomial Expansions and Conformal Maps. Univalent Functions. Bibliography. Index.

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Book SynopsisExplains how Hilbert space techniques cross the boundaries into the foundations of probability and statistics. Focuses on the theory of martingales stochastic integration, interpolation and density estimation. Includes a copious amount of problems and examples.Table of ContentsHilbert Spaces. Probability Theory. Estimating Functions. Orthogonality and Nuisance Parameters. Martingale Estimating Functions and Projected Likelihood. Stochastic Integration and Product Integrals. Estimating Functions and the Product Integral Likelihood forContinuous Time Stochastic Processes. Hilbert Spaces and Spline Density Estimation. Bibliography. Index.

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Book SynopsisThis book describes integration and measure theory for readers interested in analysis, engineering, and economics. It gives a systematic account of Riemann-Stieltjes integration and deduces the Lebesgue-Stieltjes measure from the Lebesgue-Stieltjes integral.Table of ContentsLIMITATIONS OF THE RIEMANN INTEGRAL. Limits of Integrals and Integrability. Expectations in Probability Theory. RIEMANN-STIELTJES INTEGRALS. Riemann-Stieltjes Integrals: Introduction. Characterization of Riemann-Stieltjes Integrability. Continuous Linear Functionals on C[a,b]. Riemann-Stieltjes Integrals: Further Properties. LEBESGUE-STIELTJES INTEGRALS. The Extension of the Riemann-Stieltjes Integral. Lebesgue-Stieltjes Integrals. MEASURE THEORY. sigma-Algebras and Algebras of Sets. Measurable Functions. Measures. Lebesgue-Stieltjes Measures. THE ABSTRACT LEBESGUE INTEGRAL. The Integral Associated with a Measure Space. The Lebesgue Spaces and Norms. Absolutely Continuous Measures. Linear Functionals on the Lebesgue Spaces. Product Measures and Fubini's Theorem. Lebesgue Integration and Measures on R?n. Signed Measures and Complex Measures. Differentiation. Convergence of Sequences of Functions. Measures on Locally Compact Spaces. Hausdorff Measures and Dimension. Lorentz Spaces. Appendices. Indexes.

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Book SynopsisConsists of invited papers, from internationally recognized researchers, chosen for their quality as well as their overall unity. Describes current methods along with innovative research and presents new technologies for solving problems unique to establishment surveys.Table of ContentsPartial table of contents: FRAMES AND BUSINESS REGISTERS. Defining and Classifying Statistical Units (S. Nijhowne). Changes in Populations of Statistical Units (P. Struijs & A.Willeboordse). SAMPLE DESIGN AND SELECTION. Coordination of Samples Using Permanent Random Numbers (E.Ohlsson). Business Surveys as a Network Sample (A. Johnson). DATA COLLECTION AND RESPONSE QUALITY. Designing the Data Collection Process (C. Dippo, et al.). Electronic Data Interchange (C. Ambler, et al.). DATA PROCESSING. Matching and Record Linkage (W. Winkler). Protecting Confidentiality in Business Surveys (L. Cox). WEIGHTING AND ESTIMATION. Outliers in Business Surveys (H. Lee). Combining Design-Based and Model-Based Inference (K. Brewer). PAST, PRESENT, AND FUTURE DIRECTIONS. Quality Assurance for Business Surveys (G. Griffiths & S.Linacre). Business Surveys in Ten Years' Time (J. Ryten). Index.

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Book SynopsisPresents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions.Table of ContentsFormal Power Series. Functions Analytic at a Point. Analytic Continuation. Complex Integration. Conformal Mapping. Polynomials. Partial Fractions. Bibliography. Index.

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Book SynopsisDevelops the higher parts of function theory in a unified presentation. Starts with elliptic integrals and functions and uniformization theory, continues with automorphic functions and the theory of abelian integrals and ends with the theory of abelian functions and modular functions in several variables. The last topic originates with the author and appears here for the first time in book form.Table of ContentsAUTOMORPHIC FUNCTIONS. Fractional Linear Transformations. Noneuclidean Geometry. Discontinuous Groups. Polygon Groups. Poincar Series. The Field of Automorphic Functions. Automorphic and Algebraic Functions. Algebraic Curves of Genus 0 and 1, Canonical Polygons. ABELIAN INTEGRALS. Reduction, Existence. The Period Matrix. The Modular Group. Canonical Transformation. The Theorem of Riemann and Roch. The Theorem of Abel. The Jacobi Inversion Problem. Theta Functions. The Zeros of the Theta Function. Theta Quotients. Jacobi-Abel Functions. Cumulative Index: Vols. I & II

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Book SynopsisTable of ContentsSpectral Operators. Spectral Operators: Sufficient Conditions. Algebras of Spectral Operators. Unbounded Spectral Operators. Perturbations of Spectral Operators with Discrete Spectra. Spectral Operators with Continuous Spectra: Applications of theGeneral Theory. References. Notation Index. Author Index. Subject Index.

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Book SynopsisTable of ContentsSet-theoretic Preliminaries. Toplogical Preliminaries. Algebraic Preliminaries. Three Basic Principles of Linear Analysis. Integration and Set Functions. Special Spaces. Convex Sets and Weak Topologies. Operators and Their Adjoints. General Spectral Theory. Applications. References. Notation Index. Author Index. Subject Index.

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Book SynopsisThis Second Edition of a standard numerical analysis text retains organization of the original edition, but all sections have been revised, some extensively, and bibliographies have been updated.Table of ContentsIts Sources, Propagation, and Analysis.Rootfinding for Nonlinear Equations.Interpolation Theory.Approximation of Functions.Numerical Integration.Numerical Methods for Ordinary Differential Equations.Linear Algebra.Numerical Solution of Systems of Linear Equations.The Matrix Eigenvalue Problem.Appendix.Answers to Selected Problems.Index.

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Book SynopsisThe Fifth Edition of one of the standard works on number theory, written by internationally-recognized mathematicians. Chapters are relatively self-contained for greater flexibility. New features include expanded treatment of the binomial theorem, techniques of numerical calculation and a section on public key cryptography. Contains an outstanding set of problems.Table of ContentsDivisibility. Congruences. Quadratic Reciprocity and Quadratic Forms. Some Functions of Number Theory. Some Diophantine Equations. Farey Fractions and Irrational Numbers. Simple Continued Fractions. Primes and Multiplicative Number Theory. Algebraic Numbers. The Partition Function. The Density of Sequences of Integers. Appendices. General References. Hints. Answers. Index.

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Book SynopsisIntroduces the basic principles and ideas of MACSYMA, a computer programming system designed to perform mathematical computations and manipulations in symbolic as well as numerical form.Table of ContentsGetting Started. Variables, Lists, Equations, Functions, and Arrays. Iteration, Conditionals, Blocks, and Recursion. Part Selection, Substitution, and Ev. Internal Representation, Storage, General Utilities. Matrices and Lists. Advanced Uses of MACSYMA. References. Answers to the Exercises. Index.

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Book SynopsisThis revision of a well--known text includes more sophisticated mathematical material. A new section on applications provides an introduction to the modern treatment of calculus of several variables, and the concept of duality receives expanded coverage. Notations have been changed to correspond to more current usage.Table of ContentsIntroduction. Vector Spaces. Linear Transformations and Matrics. Determinants, Eigenvalues, and Similarity Transformations. Linear Functionals, Bilinear Forms, Quadratic Forms. Orthogonal and Unitary Transformations, Normal Matrices. Selected Applications of Linear Algebra. Appendix. Answers to Selected Exercises.

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Book SynopsisImparts a self-contained development of the algebraic theory of Kac-Moody algebras, their representations and close relatives--the Virasoro and Heisenberg algebras. Focuses on developing the theory of triangular decompositions and part of the Kac-Moody theory not specific to the affine case. Also covers lattices, and finite root systems, infinite-dimensional theory, Weyl groups and conjugacy theorems.Table of ContentsLie Algebras. Lie Algebras Admitting Triangular Decompositions. Lattices and Root Systems. Contragredient Lie Algebras. The Weyl Group and Its Geometry. Category O for Kac-Moody Algebras. Conjugacy Theorems. Appendix. Bibliography. Index.

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Book SynopsisFully-worked solutions to problems encountered in the bestselling differentials text Introduction to Ordinary Differential Equations, Student Solutions Manual, 4th Edition provides solutions to practice problems given in the original textbook. Aligned chapter-by-chapter with the text, each solution provides step-by-step guidance while explaining the logic behind each step in the process of solving differential equations. From first-order equations and higher-order linear differentials to constant coefficients, series solutions, systems, approximations, and more, this solutions guide clarifies increasingly complex calculus with practical, accessible instruction.Table of ContentsDifferential Equations and Their Solutions. First-Order Equations for Which Exact Solutions AreObtainable. Applications of First-Order Equations. Explicit Methods of Solving Higher-Order Linear DifferentialEquations. Applications of Second-Order Linear Differential Equations withConstant Coefficients. Series Solutions of Linear Differential Equations. Systems of Linear Differential Equations. Approximate Methods of Solving First-Order Equations. The Laplace Transform. Appendices. Suggested Reading. Answers to Odd-Numbered Exercises. Index.

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Book SynopsisWILEY--INTERSCIENCE PAPERBACK SERIES The Wiley--Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation.Trade Review"…a significant and comprehensive resource...available in an attractive and reasonably priced format." (Technometrics, August 2005) "...an excellent addition to a six-sigma program...as well as a useful resource for the reliability engineer or student in statistics. The book is also applicable to many other fields..." (IEEE Electrical Insulation Magazine, July/August 2005) “…extremely useful for courses on life data analysis, statistical quality control and product marketing.” (Zentralblatt Math, Vol.1054, No.05, 2005)Table of ContentsPreface to the Paperback Edition. Preface. About the Author. 1. Overview and Background. 2. Basic Concepts and Distributions for Product Life. 3. Probability Plotting of Complete and Singly Censored Data. 4. Graphical Analysis of Multiply Censored Data. 5. Series Systems and Competing Risks. 6. Analysis of Complete Data. 7. Linear Methods for Singly Censored Data. 8. Maximum Likelihood Analysis of Multiply Censored Data. 9. Analyses of Inspection Data (Qualtal-Response and Interval Data). 10. Comparisons (Hypothesis Tests) For Complete Data. 11. Comparisons with Linear Estimators (Singly Censored and Complete Data). 12. Maximum Likelihood Comparisons (Multiply Censored and Other Data). 13. Survey of Other Topics. Appendix A. Tables.. References. Index.

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Book SynopsisAn introduction to the main principles of ordinary differential equations. This work exposes the roots of modern dynamical systems in order to help readers gain a foundation of ordinary differential equations; and also provides a foundation for most of the sub disciplines of differential equations and dynamical systems.Table of ContentsPreface. 1. Fundamental Theorems. 2. Classical Themes. 3. Linear Differential Equations. 4. Constant Coefficients. 5. Stability. 6. The Poincare Return Map. 7. Smooth Vector Fields. 8. Hyperbolic Phenomenon. 9. Bifurcations. Bibliography. Index.

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Book SynopsisBioremediation and Natural Attenuation: Process Fundamentals and Mathematical Models provides, under one cover, the current methodology needed by groundwater scientists and engineers in their efforts to evaluate contamination problems, to estimate risk to human health and ecosystems, and to design and formulate remediation strategies.Trade Review"…does a very good job of bringing together material form disparate sources…readers new to the field will be well served by it." (Ground Water, March-April 2007) "The topic is important; both theory and state-of-the-art are well discussed…this is an excellent book." (Journal of Hazardous Materials, September 1, 2006) “… a reference book for practitioners, regulators, and researchers dealing with contaminant hydrogeology and correction action.” (Environmental Geology, December 2006)Table of ContentsPreface. 1. Introduction to Bioremediation. 2. Geochemical Attenuation Mechanisms. 3. Biodegradation Principles. 4. Fundamentals of Ground Water Flow and Contaminant Transport Processes. 5. Fate and Transport Equations and Analytical Models for Natural Attenuation. 6. Numerical Modeling of Contaminant Transport, Transformation, and Degradation Processes. 7. Field and Laboratory Techniques to Determine Site-Specific Parameters for Modeling the Fate and Transport of Groundwater Pollutants. 8. Bioremediation Technologies. 9. Performance Assessment and Demonstration of Bioremediation and Natural Attenuation. Appendix A: Chemical Properties of Various Compounds. Appendix B: Free Energy and Thermodynamic Feasibility of Chemical and Biochemical Reactions. Appendix C: Commonly Used Numerical Groundwater Flow and Solute Transport Codes (Modified after Wiedemeier et al., 1999). Appendix D: Nonparametric Statistical Tests for Determining the Effectiveness of Natural Attenuation (after Wisconsin Department of Natural Resources). Appendix E: Critical Values of the Student t-Distribution. Glossary. Index.

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Book SynopsisA multidisciplinary approach that emphasizes learning by analyzing real-world data sets This book is the result of the authors' hands-on classroom experience and is tailored to reflect how students best learn to analyze linear relationships. The text begins with the introduction of four simple examples of actual data sets.Trade Review"…a nice reference text for programs offering a major in statistics…" (Technometrics, November 2006) "…an excellent approach to linear models and statistical interference." (CHOICE, September 2006) "...a very solid introduction to linear models." (MAA Reviews, October 19, 2005)Table of ContentsIntroduction: Statistical Questions. 1. Data: Plots and Location. 2. Data: Dispersion and Correlation. 3. Random Variables: Probability and Density. 4. Random Variables: Expectation and Variance. 5. Statistical Inference. 6. Simple Linear Models. 7. Linear Model Diagnostics. 8. Linear Models: Two Independent Variables. 9. Linear Models: Several Independent Variables. 10. Model Building. 11. Extended Linear Models. Appendix A: Data References. Appendix B: MINITAB Reference. Appendix C: Introduction to Linear Algebra. Appendix D: Statistical Tables. References. Index.

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Book SynopsisThis pioneering resource tells the full story of Fourier analysis-its history, its impact on the development of modern mathematical analysis, and today's applications. The topics are presented using a cause-and-effect approach, illustrating where ideas originated and what necessitated them.Trade Review"Eric Stade has done a great job of writing a textbook that gets across the beauty and utility of this subject." (CMS Notes, September 2005) "The author dies a great job of incorporating his sense of humor throughout this book...appealing to engineers and both applied and pure mathematicians…" (MAA Reviews, January 20, 2006) "Arguments are rigorous...and treatments are thorough...a very nice book for the intended audience." (CHOICE, November 2005)Table of ContentsPreface. Introduction. 1. Fourier Coefficients and Fourier Series. 2. Fourier Series and Boundary Value Problems. 3. L2 Spaces: Optimal Contexts for Fourier Series. 4. Sturm-Liouville Problems. 5. A Splat and a Spike. 6. Fourier Transforms and Fourier Integrals. 7. Special Topics and Applications. 8. Local Frequency Analysis and Wavelets. Appendix. References. Index.

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Book SynopsisA straightforward, practical guide to extreme value modeling for today''s world Measuring and interpreting data for extreme values presents a unique and important challenge that has far-reaching implications for all aspects of modern engineering and science. Extreme Value and Related Models with Applications in Engineering and Science reflects the latest information in this growing field. The book incorporates illuminating real-world examples from such areas as structural engineering, hydraulics, meteorology, materials science, highway traffic analysis, environmetrics, and climatology, and is designed to help engineers, mathematicians, statisticians, and scientists gain a clearer understanding of extreme value theory and then translate that knowledge into practical applications within their own fields of research. The book provides: A unique focus on modern topics including data analysis and inference Specific data in such areas as wind, flood, chain stTrade Review“This text provides an extensive coverage of the distribution theory of extreme values…the text is well presented with clearly displayed equations and diagrams…a particularly useful reference book…” (International Statistical Institute, Vol 25 (2) August 2005)Table of ContentsPreface. I: DATA, INTRODUCTION AND MOTIVATION. 1. Introduction and Motivation. II: PROBABILISTIC MODELS USEFUL IN EXTREMES. 2. Discrete Probabilistic Models. 3. Continuous Probabilistic Models. III: MODEL ESTIMATION, SELECTION, AND VALIDATION. 4. Model Estimation. 5. Model Selection and Validation. IV: EXACT MODELS FOR ORDER STATISTICS AND EXTREMES. 6. Order Statistics. 7. Point Processes and Exact Models. V: ASYMPTOTIC MODELS FOR EXTREMES AND EXCEEDANCES. 8. Limit Distributions of Order Statistics. 9. Limit Distributions of Exceedances. 10. Multivariate Extremes. Appendix: Statistical Tables. Bibliography. Index.

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Book SynopsisThe Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists.Table of ContentsForeword vii Preface ix Part One. Survey of Probability Theory Chapter 1. Introduction 3 Chapter 2. Experiments, Sample Spaces, and Probability 6 Chapter 3. Random Variables, Random Vectors, and Distribution Functions 16 Chapter 4. Some Special Univariate Distributions 33 Chapter 5. Some Special Multivariate Distributions 48 Part Two. Subjective Probability and Utility Chapter 6. Subjective Probability 69 Chapter 7. Utility 86 Part Three. Statistical Decision Problems Chapter 8. Decision Problems 121 Chapter 9. Conjugate Prior Distributions 155 Chapter 10. Limiting Posterior Distributions 190 Chapter 11. Estimation, Testing Hypotheses, and linear Statistical Models 226 Part Four. Sequential Decisions Chapter 12. Sequential Sampling 267 Chapter 13. Optimal Stopping 324 Chapter 14. Sequential Choice of Experiments 385 References 447 Supplementary Bibliography 466 Name Index 475 Subject Index 481

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Book SynopsisA visually intuitive approach to statistical data analysis Visual Statistics brings the most complex and advanced statistical methods within reach of those with little statistical training by using animated graphics of the data. Using ViSta: The Visual Statistics System-developed by Forrest Young and Pedro Valero-Mora and available free of charge on the Internet-students can easily create fully interactive visualizations from relevant mathematical statistics, promoting perceptual and cognitive understanding of the data''s story. An emphasis is placed on a paradigm for understanding data that is visual, intuitive, geometric, and active, rather than one that relies on convoluted logic, heavy mathematics, systems of algebraic equations, or passive acceptance of results. A companion Web site complements the book by further demonstrating the concept of creating interactive and dynamic graphics. The book provides users with the opportunity to view the graphics in a Trade Review"With contributions by highly regarded professionals in the field, Visual Statistics not only improves a student's understanding of statistics, but also builds condence to overcome problems that may have previously been intimidating." (Zentralblatt MATH 2016) "A good book about a great software system." (Psychometrika, March 2008) "The people who would benefit most from this book are those who teach courses in statistics." (AstA Advances in Statistical Analysis, 2008) "... the book admirably guides readers through the process of exploring and analyzing a variety of types of data." (The American Statistician, August 2007) "A technically well-produced book, significant in that it documents efforts these psychometrics faculty made in using visual approaches to analyze data." (CHOICE, March 2007) "... covers its subject matter skillfully, and provides great insight into the world of the dynamic visualization of statistical data." (Journal of Applied Statistics, 2007) "Forrest Young has been a leading light in developing dynamic interactive graphics for decades... so [I] am delighted to see this book appear." (Short Book Reviews, December 2006) "... the book not only improves a student's understanding of statistics, but also builds confidence to overcome problems that may have previously been intimidating... an excellent textbook" (Computing Reviews.com, November 16, 2006)Table of ContentsPart I Introduction 1 Introduction 1.1 Visual Statistics 6 1.2 Dynamic Interactive Graphies 7 1.2.1 An Analogy 7 1.2.2 Why Use Dynamic Graphies? 8 1.2.3 The Four Respects 8 1.3 Three Examples 9 1.3.1 Nonrandom Numbers 9 1.3.2 Automobile Efficiency 11 1.3.3 Fidelity and Marriage 14 1.4 History of Statistical Graphics 18 1.4.1 1600-1699: Measurement and Theory 18 1.4.2 1700-1799: New Graphic Forms and Data 19 1.4.3 1800-1899: Modern Graphics and the Golden Age 20 1.4.4 1900-1950: The Dark Ages of Statistical Graphics—The Golden Age of Mathematical Statistics 21 1.4.5 1950-1975: Rebirth of Statistical Graphics 22 1.4.6 1975-2000: Statistical Graphics Comes of Age 23 1.5 About Software 24 1.5.1 XLisp-Stat 25 1.5.2 Commercial Systems 26 1.5.3 Noncommercial Systems 26 1.5.4 ViSta 27 1.6 About Data 29 1.6.1 Essential Characteristics 30 1.6.2 Datatypes 32 1.6.3 Datatype Examples 34 1.7 About This Book 34 1.7.1 What This Book Is—and Isn't 34 1.7.2 Organization 34 1.7.3 Who Our Audience Is—and Isn't 37 1.7.4 Comics 38 1.7.5 Thumb-Powered Dynamic Graphics 39 1.8 Visual Statistics and the Graphical User Interface 40 1.9 Visual Statistics and the Scientific Method 40 1.9.1 A Paradigm for Seeing Data 41 1.9.2 About Statistical Data Analysis: Visual or Otherwise 42 2 Examples 45 2.1 Random Numbers 47 2.2 Medical Diagnosis 52 2.3 Fidelity and Marriage 59 Part II See Data—The Process 3 Interfaces and Environments 73 3.1 Objects 77 3.2 User Interfaces for Seeing Data 78 3.3 Character-Based Statistical Interface Objects 79 3.3.1 Command Line 79 3.3.2 Calculator 80 3.3.3 Program Editor 80 3.3.4 Report Generator 81 3.4 Graphics-Based Statistical Interfaces 81 3.4.1 Datasheets 81 3.4.2 Variable Window 82 3.4.3 Desktop 82 3.4.4 Workmap 83 3.4.5 Selector 87 3.5 Plots 88 3.5.1 Look of Plots 89 3.5.2 Feel of Plots 91 3.5.3 Impact of Plot Look and Feel 93 3.6 Spreadplots 94 3.6.1 Layout 96 3.6.2 Coordination 98 3.6.3 SpreadPlots 100 3.6.4 Look of Spreadplots 102 3.6.5 Feel of Spreadplots 104 3.6.6 Look and Feel of Statistical Data Analysis 104 3.7 Environments for Seeing Data 111 3.8 Sessions and Projects 114 3.9 The Next Reality 114 3.9.1 The Fantasy 114 3.9.2 The Reality 116 3.9.3 Reality Check 118 4 Tools and Techniques 119 4.1 Types of Controls 123 4.1.1 Buttons 123 4.1.2 Palettes 125 4.1.3 Menus and Menu Items 125 4.1.4 Dialog Boxes 125 4.1.5 Sliders 126 4.1.6 Control Panels 127 4.1.7 The Plot Itself 127 4.1.8 Hyperlinking 127 4.2 Datasheets 128 4.3 Plots 129 4.3.1 Activating Plot Objects 131 4.3.2 Manipulating Plot Objects 132 4.3.3 Manipulating Plot Dimensions 138 4.3.4 Adding Graphical Elements 141 Part III Seeing Data—Objects 5 Seeing Frequency Data 145 5.1 Data 148 5.1.1 Automobile Efficiency: 148 5.1.2 Berkeley Admissions Data 148 5.1.3 Tables of Frequency data 150 5.1.4 Working at the Categories Level 151 5.1.5 Working at the Variables Level 153 5.2 Frequency Plots 157 5.2.1 Mosaic Displays 157 5.2.2 Dynamic Mosaic Displays 159 5.3 Visual Fitting of Log-Linear Models 164 5.3.1 Log-Linear Spreadplot 165 5.3.2 Specifying Log-Linear Models and the Model Builder Window 166 5.3.3 Evaluating the Global Fit of Models and Their History 170 5.3.4 Visualizing Fitted and Residual Values with Mosaic Displays 174 5.3.5 Interpreting the Parameters of the Model 176 5.4 Conclusions 179 6 Seeing Univariate Data 181 6.1 Introduction 183 6.2 Data: Automobile Efficiency 185 6.2.1 Looking at the Numbers 186 6.2.2 What Can Unidimensional Methods Reveal? 186 6.3 Univariate Plots 190 6.3.1 Dotplots 190 6.3.2 Boxplots 193 6.3.3 Cumulative Distribution Plots 196 6.3.4 Histograms and Frequency Polygons 199 6.3.5 Ordered Series Plots 208 6.3.6 Namelists 209 6.4 Visualization for Exploring Univariate Data 209 6.5 What Do We See in MPG1 212 7 Seeing Bivariate Data 215 7.1 Introduction 217 7.1.1 Plots About Relationships 217 7.1.2 Chapter Preview 220 7.2 Data: Automobile Efficiency 221 7.2.1 What the Data Seem to Say 222 7.3 Bivariate Plots 224 7.3.1 Scatterplots 224 7.3.2 Distribution Comparison Plots 233 7.3.3 Parallel-Coordinates Plots and Parallel Boxplots 236 7.4 Multiple Bivariate Plots 236 7.4.1 Scatterplot Plot Matrix 2377.4.2 Quantile Plot Matrix 238 7.4.3 Numerical Plot-matrix 238 7.4.4 BoxPlot Plot Matrix 239 7.5 Bivariate Visualization Methods 241 7.6 Visual Exploration 242 7.6.1 Two Bivariate Data Visualizations 243 7.6.2 Using These Visualizations 245 7.7 Visual Transformation: Box-Cox 247 7.7.1 The Transformation Visualization 249 7.7.2 Using Transformation Visualization 251 7.7.3 The Box-Cox Power Transformation 255 7.8 Visual Fitting: Simple Regression 256 7.9 Conclusions 260 8 Seeing Multivariate Data 263 8.1 Data: Medical Diagnosis 266 8.2 Three Families of Multivariate Plots 270 8.3 Parallel-Axes Plots 272 8.3.1 Parallel-Coordinates Plot 272 8.3.2 Parallel-Comparisons Plot 276 8.3.3 Parallel Univariate Plots 277 8.4 Orthogonal-Axes Plots 279 8.4.1 Spinplot 280 8.4.2 Orbitplot 283 8.4.3 BiPlot 286 8.4.4 Wiggle-Worm (Multivariable Comparison) Plot 291 8.5 Paired-Axes Plots 292 8.5.1 Spinplot Plot Matrix 293 8.5.2 Parallel-Coordinates Plot Matrix 294 8.6 Multivariate Visualization 295 8.6.1 Variable Visualization 295 8.6.2 Principal Components Analysis 296 8.6.3 Fit Visualization 298 8.6.4 Principal Components Visualization 300 8.6.5 One More Step - Discriminant Analysis 302 8.7 Summary 304 8.7.1 What Did We See? Clusters! 304 8.7.2 How Did We See It? 304 8.7.3 How Do We Interpret It? With Diagnostic Groups! 305 8.8 Conclusion 306 9 Seeing Missing Values 309 9.1 Introduction 312 9.2 Data: Sleep in Mammals 314 9.3 Missing Data Visualization Tools 315 9.3.1 Missing Values Bar Charts 316 9.3.2 Histograms and Bar Charts 316 9.3.3 Boxplots 316 9.3.4 Scatterplots 316 9.4 Visualizing Imputed Values 317 9.4.1 Marking the Imputed Values 318 9.4.2 Single Imputation 320 9.4.3 Multiple Imputation 325 9.4.4 Summary of Imputation 327 9.5 Missing Data Patterns 327 9.5.1 Patterns and Number of Cases 328 9.5.2 The Mechanisms Leading to Missing Data 329 9.5.3 Visualizing Dynamically the Patterns of Missing Data 331 9.6 Conclusions 337 References 339 Author Index 351 Subject Index 355

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Book SynopsisThe purpose of this book is to introduce the theory of U-Statistics and illustrate it with a wide range of timely applications arising in genetics, biomedical, and psychological research.Table of ContentsPreface. 1. Preliminaries. 2. Models for Cross-Sectional Data. 3. Univariate U-Statistics. 4. Models for Clustered Data. 5. Multivariate U-Statistics. 6. Functional response Models. References. Subject Index.

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Book SynopsisStatistical Intervals is a guide for practitioners and researchers--providing a detailed, comprehensive, modernized treatment of this important subject. With numerous examples, it presents and differentiates in an easy-to-apply manner the use of confidence intervals (e.g.Table of ContentsPreface to Second Edition iii Preface to First Edition vii Acknowledgments x 1 Introduction, Basic Concepts, and Assumptions 1 1.1 Statistical Inference 2 1.2 Different Types of Statistical Intervals: An Overview 2 1.3 The Assumption of Sample Data 3 1.4 The Central Role of Practical Assumptions Concerning Representative Data 4 1.5 Enumerative Versus Analytic Studies 5 1.6 Basic Assumptions for Enumerative Studies 7 1.7 Considerations in the Conduct of Analytic Studies 10 1.8 Convenience and Judgment Samples 11 1.9 Sampling People 12 1.10 Infinite Population Assumptions 13 1.11 Practical Assumptions: Overview 14 1.12 Practical Assumptions: Further Example 14 1.13 Planning the Study 17 1.14 The Role of Statistical Distributions 17 1.15 The Interpretation of Statistical Intervals 18 1.16 Statistical Intervals and Big Data 19 1.17 Comment Concerning Subsequent Discussion 19 2 Overview of Different Types of Statistical Intervals 21 2.1 Choice of a Statistical Interval 21 2.2 Confidence Intervals 23 2.3 Prediction Intervals 24 2.4 Statistical Tolerance Intervals 26 2.5 Which Statistical Interval Do I Use? 27 2.6 Choosing a Confidence Level 28 2.7 Two-Sided Statistical Intervals Versus One-Sided Statistical Bounds 29 2.8 The Advantage of Using Confidence Intervals Instead of Significance Tests 30 2.9 Simultaneous Statistical Intervals 31 3 Constructing Statistical Intervals Assuming a Normal Distribution Using Simple Tabulations 33 3.1 Introduction 34 3.2 Circuit Pack Voltage Output Example 35 3.3 Two-Sided Statistical Intervals 36 3.4 One-Sided Statistical Bounds 38 4 Methods for Calculating Statistical Intervals for a Normal Distribution 43 4.1 Notation 44 4.2 Confidence Interval for the Mean of a Normal Distribution 45 4.3 Confidence Interval for the Standard Deviation of a Normal Distribution 45 4.4 Confidence Interval for a Normal Distribution Quantile 46 4.5 Confidence Interval for the Distribution Proportion Less (Greater) Than a Specified Value 47 4.6 Statistical Tolerance Intervals 48 4.7 Prediction Interval to Contain a Single Future Observation or the Mean of m Future Observations 50 4.8 Prediction Interval to Contain at least k of m Future Observations 51 4.9 Prediction Interval to Contain the Standard Deviation of m Future Observations 52 4.10 The Assumption of a Normal Distribution 53 4.11 Assessing Distribution Normality and Dealing with Nonnormality 54 4.12 Data Transformations and Inferences from Transformed Data 57 4.13 Statistical Intervals for Linear Regression Analysis 60 4.14 Statistical Intervals for Comparing Populations and Processes 62 5 Distribution-Free Statistical Intervals 65 5.1 Introduction 66 5.2 Distribution-Free Confidence Intervals and One-Sided Confidence Bounds for a Quantile 68 5.3 Distribution-Free Tolerance Intervals and Bounds to Contain a Specified Proportion of a Distribution 78 5.4 Prediction Intervals to Contain a Specified Ordered Observation in a Future Sample 81 5.5 Distribution-Free Prediction Intervals and Bounds to Contain at Least k of m Future Observations 84 6 Statistical Intervals for a Binomial Distribution 89 6.1 Introduction to Binomial Distribution Statistical Intervals 90 6.2 Confidence Intervals for the Actual Proportion Nonconforming in the Sampled Distribution 92 6.3 Confidence Interval for the Proportion of Nonconforming Units in a Finite Population 102 6.4 Confidence Intervals for the Probability that the Number of Nonconforming Units in a Sample is Less than or Equal to (or Greater than) a Specified Number 104 6.5 Confidence Intervals for the Quantile of the Distribution of the Number of Nonconforming Units 105 6.6 Tolerance Intervals and One-Sided Tolerance Bounds for the Distribution of the Number of Nonconforming Units 107 6.7 Prediction Intervals for the Number Nonconforming in a Future Sample 108 7 Statistical Intervals for a Poisson Distribution 115 7.1 Introduction 116 7.2 Confidence Intervals for the Event-Occurrence Rate of a Poisson Distribution 117 7.3 Confidence Intervals for the Probability that the Number of Events in a Specified Amount of Exposure is Less than or Equal to (or Greater than) a Specified Number 124 7.4 Confidence Intervals for the Quantile of the Distribution of the Number of Events in a Specified Amount of Exposure 125 7.5 Tolerance Intervals and One-Sided Tolerance Bounds for the Distribution of the Number of Events in a Specified Amount of Exposure 127 7.6 Prediction Intervals for the Number of Events in a Future Amount of Exposure 128 8 Sample Size Requirements for Confidence Intervals on Distribution Parameters 135 8.1 Basic Requirements for Sample Size Determination 136 8.2 Sample Size for a Confidence Interval for a Normal Distribution Mean 137 8.3 Sample Size to Estimate a Normal Distribution Standard Deviation 141 8.4 Sample Size to Estimate a Normal Distribution Quantile 143 8.5 Sample Size to Estimate a Binomial Proportion 143 8.6 Sample Size to Estimate a Poisson Occurrence Rate 144 9 Sample Size Requirements for Tolerance Intervals, Tolerance Bounds, and Related Demonstration Tests 148 9.1 Sample Size for Normal Distribution Tolerance Intervals and One-Sided Tolerance Bounds148 9.2 Sample Size to Pass a One-Sided Demonstration Test Based on Normally Distributed Measurements 150 9.3 Minimum Sample Size For Distribution-Free Two-Sided Tolerance Intervals and One-Sided Tolerance Bounds 152 9.4 Sample Size for Controlling the Precision of Two-Sided Distribution-Free Tolerance In-tervals and One-Sided Distribution-Free Tolerance Bounds 153 9.5 Sample Size to Demonstrate that a Binomial Proportion Exceeds (is Exceeded by) a Specified Value 154 10 Sample Size Requirements for Prediction Intervals 164 10.1 Prediction Interval Width: The Basic Idea 164 10.2 Sample Size for a Normal Distribution Prediction Interval 165 10.3 Sample Size for Distribution-Free Prediction Intervals for k of m Future Observations 170 11 Basic Case Studies 172 11.1 Demonstration that the Operating Temperature of Most Manufactured Devices will not Exceed a Specified Value 173 11.2 Forecasting Future Demand for Spare Parts 177 11.3 Estimating the Probability of Passing an Environmental Emissions Test 180 11.4 Planning a Demonstration Test to Verify that a Radar System has a Satisfactory Prob-ability of Detection 182 11.5 Estimating the Probability of Exceeding a Regulatory Limit 184 11.6 Estimating the Reliability of a Circuit Board 189 11.7 Using Sample Results to Estimate the Probability that a Demonstration Test will be Successful 191 11.8 Estimating the Proportion within Specifications for a Two-Variable Problem 194 11.9 Determining the Minimum Sample Size for a Demonstration Test 195 12 Likelihood-Based Statistical Intervals 197 12.1 Introduction to Likelihood-Based Inference 198 12.2 Likelihood Function and Maximum Likelihood Estimation 200 12.3 Likelihood-Based Confidence Intervals for Single-Parameter Distributions 203 12.4 Likelihood-Based Estimation Methods for Location-Scale and Log-Location-Scale Distri-butions 206 12.5 Likelihood-Based Confidence Intervals for Parameters and Scalar Functions of Parameters212 12.6 Wald-Approximation Confidence Intervals 216 12.7 Some Other Likelihood-Based Statistical Intervals 224 13 Nonparametric Bootstrap Statistical Intervals 226 13.1 Introduction 227 13.2 Nonparametric Methods for Generating Bootstrap Samples and Obtaining Bootstrap Estimates 227 13.3 Bootstrap Operational Considerations 231 13.4 Nonparametric Bootstrap Confidence Interval Methods 233 14 Parametric Bootstrap and Other Simulation-Based Statistical Intervals 245 14.1 Introduction 246 14.2 Parametric Bootstrap Samples and Bootstrap Estimates 247 14.3 Bootstrap Confidence Intervals Based on Pivotal Quantities 250 14.4 Generalized Pivotal Quantities 253 14.5 Simulation-Based Tolerance Intervals for Location-Scale or Log-Location-Scale Distribu-tions 258 14.6 Simulation-Based Prediction Intervals and One-Sided Prediction Bounds for k of m Fu-ture Observations from Location-Scale or Log-Location-Scale Distributions 260 14.7 Other Simulation and Bootstrap Methods and Application to Other Distributions and Models 263 15 Introduction to Bayesian Statistical Intervals 270 15.1 Bayesian Inference: Overview 271 15.2 Bayesian Inference: an Illustrative Example 274 15.3 More About Specification of a Prior Distribution 283 15.4 Implementing Bayesian Analyses Using Markov Chain Monte Carlo Simulation 286 15.5 Bayesian Tolerance and Prediction Intervals 291 16 Bayesian Statistical Intervals for the Binomial, Poisson and Normal Distributions 297 16.1 Bayesian Intervals for the Binomial Distribution 298 16.2 Bayesian Intervals for the Poisson Distribution 306 16.3 Bayesian Intervals for the Normal Distribution 311 17 Statistical Intervals for Bayesian Hierarchical Models 321 17.1 Bayesian Hierarchical Models and Random Effects 322 17.2 Normal Distribution Hierarchical Models 323 17.3 Binomial Distribution Hierarchical Models 325 17.4 Poisson Distribution Hierarchical Models 328 17.5 Longitudinal Repeated Measures Models 329 18 Advanced Case Studies 335 18.1 Confidence Interval for the Proportion of Defective Integrated Circuits 336 18.2 Confidence Intervals for Components of Variance in a Measurement Process 339 18.3 Tolerance Interval to Characterize the Distribution of Process Output in the Presence of Measurement Error 344 18.4 Confidence Interval for the Proportion of Product Conforming to a Two-Sided Specification345 18.5 Confidence Interval for the Treatment Effect in a Marketing Campaign 348 18.6 Confidence Interval for the Probability of Detection with Limited Hit-Miss Data 349 18.7 Using Prior Information to Estimate the Service-Life Distribution of a Rocket Motor 353 Epilogue 357 A Notation and Acronyms 360 B Generic Definition of Statistical Intervals and Formulas for Computing Coverage Probabilities 367 B.1 Introduction 367 B.2 Two-sided Confidence Intervals and One-sided Confidence Bounds for Distribution Pa-rameters or a Function of Parameters 368 B.3 Two Sided Control-the-Center Tolerance Intervals to Contain at Least a Specified Pro-portion of a Distribution 371 B.4 Two Sided Tolerance Intervals to Control Both Tails of a Distribution 374 B.5 One-Sided Tolerance Bounds 377 B.6 Two-sided Prediction Intervals and One-Sided Prediction Bounds for Future Observations378 B.7 Two-Sided Simultaneous Prediction Intervals and One-Sided Simultaneous Prediction Bounds 381 B.8 Calibration of Statistical Intervals 383 C Useful Probability Distributions 384 C.1 Probability Distribution and R Computations 384 C.2 Important Characteristics of Random Variables 385 C.3 Continuous Distributions 388 C.4 Discrete Distributions 398 D General Results from Statistical Theory and Some Methods Used to Construct Sta-tistical Intervals 404 D.1 cdfs and pdfs of Functions of Random Variables 405 D.2 Statistical Error Propagation—The Delta Method 409 D.3 Likelihood and Fisher Information Matrices 410 D.4 Convergence in Distribution 413 D.5 Outline of General ML Theory 415 D.6 The CDF pivotal method for constructing confidence intervals 419 D.7 Bonferroni approximate statistical intervals 424 E Pivotal Methods for Constructing Parametric Statistical Intervals 427 E.1 General definition and examples of pivotal quantities 428 E.2 Pivotal Quantities for the Normal Distribution 428 E.3 Confidence intervals for a Normal Distribution Based on Pivotal Quantities 429 E.4 Confidence Intervals for Two Normal Distributions Based on Pivotal Quantities 432 E.5 Tolerance Intervals for a Normal Distribution Based on Pivotal Quantities 432 E.6 Normal Distribution Prediction Intervals Based on Pivotal Quantities 434 E.7 Pivotal Quantities for Log-Location-Scale Distributions 436 F Generalized Pivotal Quantities 440 F.1 Definition of Generalized Pivotal Quantities 440 F.2 A Substitution Method to Obtain GPQs 441 F.3 Examples of GPQs for Functions of Location-Scale Distribution Parameters 441 F.4 Conditions for Exact Intervals Derived from GPQs 443 G Distribution-Free Intervals Based on Order Statistics 446 G.1 Basic Statistical Results Used in this Appendix 446 G.2 Distribution-Free Confidence Intervals and Bounds for a Distribution Quantile 447 G.3 Distribution-Free Tolerance Intervals to Contain a Given Proportion of a Distribution 448 G.4 Distribution-Free Prediction Interval to Contain a Specified Ordered Observation From a Future Sample 449 G.5 Distribution-Free Prediction Intervals and Bounds to Contain at Least k of m Future Observations From a Future Sample 451 H Basic Results from Bayesian Inference Models 455 H.1 Basic Statistical Results Used in this Appendix 455 H.2 Bayes’ Theorem 456 H.3 Conjugate Prior Distributions 456 H.4 Jeffreys Prior Distributions 459 H.5 Posterior Predictive Distributions 463 H.6 Posterior Predictive Distributions Based on Jeffreys Prior Distributions 465 I Probability of Successful Demonstration 468 I.1 Demonstration Tests Based on a Normal Distribution Assumption 468 I.2 Distribution-Free Demonstration Tests 469 J Tables 471 References 508 Subject Index 525

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Book SynopsisAvailable in paperback for the first time, this bestseller provides a systematic account of the subject area, while concentrating on the most recent advances in the field. While the focus is on practical considerations, both theoretical and practical issues are explored.Trade Review“ … in my opinion (this book) has been proved .. to be a valuable resource (and) should not be overlooked by any scholarly library.” (Journal of the Royal Statistical Society Series A, June 2005)Table of ContentsPreface. 1. General Introduction. 2. Likelihood-Based Approaches to Discrimination. 3. Discrimination via Normal Models. 4. Distributional Results for Discrimination via Normal Models. 5. Some Practical Aspects and Variants of Normal Theory-Based Discriminant Rules. 6. Data Analytic Considerations with Normal Theory-Based Discriminant Analysis. 7. Parametric Discrimination via Nonnormal Models. 8. Logistic Discrimination. 9. Nonparametric Discrimination. 10. Estimation of Error Rates. 11. Assessing the Reliability of the Estimated Posterior Probabilities of Group Membership. 12. Selection of Feature Variables in Discriminan Analysis. 13. Statistical Image Analysis. References. Author Index. Subject Index.

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Book SynopsisPresents the first comprehensive guide to the analysis of spatial data. Each chapter covers a particular data format and the associated class of problems, introducing theory, giving computational suggestions, and providing examples. Methods are illustrated by computer-drawn figures.Table of Contents1. Introduction. 2. Basic Stochastic Processes. 3. Spatial Sampling. 4. Smoothing and Interpolation. 5. Regional and Lattice Data. 6. Quadrat Counts. 7. Field Methods for Point Patterns. 8. Mapped Point Patterns. 9. Image Analysis and Stereology. Bibliography. Author Index. Subject Index.

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Book SynopsisProvides practicing statisticians and econometricians with fresh tools for assessing quality and reliability of regression estimates.Table of Contents1. Introduction and Overview. 2. Detecting Influential Observations and Outliers. 3. Detecting and Assessing Collinearity. 4. Applications and Remedies. 5. Research Issues and Directions for Extensions. Bibliography. Author Index. Subject Index.

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Book SynopsisAddresses basic aspects of research design which are central and common to many related fields in the social sciences, in health sciences, in education, and in market research. This work presents a unified approach to a common core of problems of statistical design that exists in these fields, along with basic similarities in practical solutions.Table of ContentsChapter and Section Contents. Tables and Figures. 1. Representation, Randomization, and Realism. 1.1 Three Criteria. 1.2 Four Classes of Variables. 1.3 Surveys, Experiments, and Controlled Investigations. 1.4 Randomization of Subjects Over Treatments and Over Populations. 1.5 Statistical Tests. 1.6 An Ordered List of Research Designs. 1.7 Representation and Probability Sampling. 1.8 Model-Dependent Inference. 2. Analytical Use of Sample Surveys. 2.1 Populations of Elements and Sampling Units. 2.2 Inferences from Complex Samples. 2.3 Domains and Subclasses: Classifications. 2.4 Overview of Subclass Effects. 2.5 Proportionate Stratified Element Sampling (PRES). 2.6 Cluster Sampling. 2.7 Four Obstacles to Representation in Analytic Studies. 3. Designs for Comparisons. 3.1 Substitutes for Probability Sampling. 3.2 Basic Modules for Comparisons. 3.3 Four Modules: Costs, Variances, Bias Sources. 3.4 Five Basic Designs for Comparisons. 3.5 Classification for 22 Sources of Bias. 3.6 Time Curves of Responses. 3.7 Evaluation Research. 4. Controls for Disturbing Variables. 4.1 Control Strategies. 4.2 Analysis in Separate Subclasses. 4.3 Selecting Matched Units. 4.4 Matched Subclasses. 4.5 Standardization: Adjustment by Weighting Indexes. 4.6 Covariances and Residuals from Linear Regressions; Categorical Data Analyses. 4.7 Ratio Estimates. 5. Samples and Censuses. 5.1 Censuses and Researchers. 5.2 Samples Compared to Censuses. 5.3 Samples Attached to Censuses. 6. Sample Designs Over Time. 6.1 Technology and Concepts. 6.2 Purposes and Designs for Periodic Samples. 6.3 Changing and Mobile Populations. 6.4 Panel Effects. 6.5 Split-Panel Designs. 6.6 Cumulating Cases and Combining Statistics from Samples. 7. Several Distinct Problems of Design. 7.1 Analytical Statistics from Complex Samples. 7.2 Generalizations Beyond the Modules of 3.3. 7.3 Multipurpose Designs. 7.4 Weighted Means: Selection, Bias, Variance. 7.5 Observational Units of Variable Sizes. 7.6 On Falsifiability in Statistical Design. Problems. References. Index.

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Book SynopsisReflecting emerging principles and trends, Measurement Errors in Surveys documents the current state of measurement errors in surveys; reports new research findings; and promotes interdisciplinary exchanges in numerous approaches in assessing, modeling and reducing measurement inaccuracies in surveys.Table of ContentsPreface. Introduction (W. Kruskal). 1. Measurement Error Across Disciplines (R. Groves). SECTION A: THE QUESTIONAIRE. 2. The Current Status of Questionnaire Design (N. Bradburn & S. Sudman). 3. Response Alternatives: The Impact of Their Choice and Presentation Order (N. Schwarz & H. Hippler). 4. Context Effects in the General Social Survey (T. Smith). 5. Mode Effects of Cognitively Designed Recall Questions: A Comparison of Answers to Telephone and Mail Surveys (D. Dillman & J. Tarnai). 6. Nonexperimental Research on Question Wording Effects: A Contribution to Solving the Generalizability Problem (N. Molenaar). 7. Measurement Errors in Business Surveys (S. Dutka & L. Frankel). SECTION B: RESPONDENTS AND RESPONSES. 8. Recall Error: Sources and Bias Reduction Techniques (D. Eisenhower, et al.). 9. Measurement Effects in Self vs. Proxy Response to Survey Questions: An Information-Processing Perspective (J. Blair, et al.). 10. An Alternative Approach to Obtaining Personal History Data (B. Means, et al.). 11. The Item Count Technique as a Method of Indirect Questioning: A Review of Its Development and a Case Study Application (J. Droitcour, et al.). 12. Toward a Response Model in Establishment Surveys (W. Edwards & D. Cantor). SECTION C: INTERVIEWERS AND OTHER MEANS OF DATA COLLECTION. 13. Data Collection Methods and Measurement Error: An Overview (L. Lyberg & D. Kasprzyk). 14. Reducing Inte5rviewer-Related Error Through Interviewer Training, Supervision, and Other Means (F. Fowler). 15. The Design and Analysis of Reinterview: An Overview (G. Forsman & I. Schreiner). 16. Expenditure Diary Surveys and Their Associated Errors (A. Silberstein & S. Scott). 17. A Review of Errors of Direct Observation in Crop Yield Surveys (R. Fecso). 18. Measurement Error in Continuing Surveys of the Grocery Retail Trade Using Electronic Data Collection Methods (J. Donmyer, et al.). SECTION D: MEASUREMENT ERRORS IN THE INTERVIEW PROCESS. 19. Conversation with a Purpose—or Conversation? Interaction in the Standardized Interview (N. Schaeffer). 20. Cognitive Laboratory Methods: A Taxonomy (B. Forsyth & J. Lessler). 21. Studying Respondent-Interviewer Interaction: The Relationship Between Interviewing Style, Interviewer Behavior, and Response Behavior (J. van der Zouwen, et al.). 22. The Effect of Interviewer and Respondent Characteristics on the Quality of Survey Data: A Multilevel Model (J. Hox, et al.). 23. Interviewer, Respondent, and Regional Office Effects on Response Variance: A Statistical Decomposition (D. Hill). SECTION E: MODELING MEASUREMENT ERRORS AND THEIR EFFECTS ON ESTIMATION AND DATA ANALYSIS. 24. Approaches to the Modeling of Measurement Errors (P. Biemer & L. Stokes). 25. A Mixed Model for Analyzing Measurement Errors for Dichotomous Variables (J. Pannekoek). 26. Models for Memory Effects in Count Data (P. van Dosselaar). 27. Simple Response Variance: Estimation and Determinants (C. O'Muircheartaigh). 28. Evaluation of Measurement Instruments Using a Structural Modeling Approach (W. Saris & F. Andrews). 29. A Path Analysis of Cross-National Data Taking Measurement Errors Into Account (I. Munck). 30. Regression Estimation in the Presence of Measurement Error (W. Fuller). 31. Chi-Squared Tests with Complex Survey Data Subject to Misclassification Error (J. Rao & D. Thomas). 32. The Effect of Measurement Error on Event History Analysis (D. Holt, et al.). References. Index.

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Book SynopsisThis book examines applications of Fourier analysis on finite non-Abelian groups, and discusses different methods to determine compact representations for discrete functions providing for their efficient realizations and related applications. Switching functions are included as a particular example of discrete functions in engineering practice.Trade Review"…a concise monograph about the algebraic structures theory used in the Fourier analysis of signals and systems…useful for applied mathematicians and for engineers…" (Computing Reviews.com, November 3, 2005)Table of ContentsPreface. Acknowledgments. Acronyms. 1 Signals and Their Mathematical Models. 1.1 Systems. 1.2 Signals. 1.3 Mathematical Models of Signals. References. 2 Fourier Analysis. 2.1 Representations of Groups. 2.1.1 Complete Reducibility. 2.2 Fourier Transform on Finite Groups. 2.3 Properties of the Fourier Transform. 2.4 Matrix Interpretation of the Fourier Transform on Finite Non-Abelian Groups. 2.5 Fast Fourier Transform on Finite Non-Abelian Groups. References. 3 Matrix Interpretation of the FFT. 3.1 Matrix Interpretation of FFT on Finite Non-Abelian Groups. 3.2 Illustrative Examples. 3.3 Complexity of the FFT. 3.3.1 Complexity of Calculations of the FFT. 3.3.2 Remarks on Programming Implememtation of FFT. 3.4 FFT Through Decision Diagrams. 3.4.1 Decision Diagrams. 3.4.2 FFT on Finite Non-Abelian Groups Through DDs. 3.4.3 MMTDs for the Fourier Spectrum. 3.4.4 Complexity of DDs Calculation Methods. References. 4 Optimization of Decision Diagrams. 4.1 Reduction Possibilities in Decision Diagrams. 4.2 Group-Theoretic Interpretation of DD. 4.3 Fourier Decision Diagrams. 4.3.1 Fourier Decision Trees. 4.3.2 Fourier Decision Diagrams. 4.4 Discussion of Different Decompositions. 4.4.1 Algorithm for Optimization of DDs. 4.5 Representation of Two-Variable Function Generator. 4.6 Representation of Adders by Fourier DD. 4.7 Representation of Multipliers by Fourier DD. 4.8 Complexity of NADD. 4.9 Fourier DDs with Preprocessing. 4.9.1 Matrix-valued Functions. 4.9.2 Fourier Transform for Matrix-Valued Functions. 4.10 Fourier Decision Trees with Preprocessing. 4.11 Fourier Decision Diagrams with Preprocessing. 4.12 Construction of FNAPDD. 4.13 Algorithm for Construction of FNAPDD. 4.13.1 Algorithm for Representation. 4.14 Optimization of FNAPDD. References. 5 Functional Expressions on Quaternion Groups. 5.1 Fourier Expressions on Finite Dyadic Groups. 5.1.1 Finite Dyadic Groups. 5.2 Fourier Expressions on Q2. 5.3 Arithmetic Expressions. 5.4 Arithmetic Expressions from Walsh Expansions. 5.5 Arithmetic Expressions on Q2. 5.5.1 Arithmetic Expressions and Arithmetic-Haar Expressions. 5.5.2 Arithmetic-Haar Expressions and Kronecker Expressions. 5.6 Different Polarity Polynomials Expressions. 5.6.1 Fixed-Polarity Fourier Expressions in C(Q2). 5.6.2 Fixed-Polarity Arithmetic-Haar Expressions. 5.7 Calculation of the Arithmetic-Haar Coefficients. 5.7.1 FFT-like Algorithm. 5.7.2 Calculation of Arithmetic-Haar Coefficients Through Decision Diagrams. References. 6 Gibbs Derivatives on Finite Groups. 6.1 Definition and Properties of Gibbs Derivatives on Finite Non-Abelian Groups. 6.2 Gibbs Anti-Derivative. 6.3 Partial Gibbs Derivatives. 6.4 Gibbs Differential Equations. 6.5 Matrix Interpretation of Gibbs Derivatives. 6.6 Fast Algorithms for Calculation of Gibbs Derivatives on Finite Groups. 6.6.1 Complexity of Calculation of Gibbs Derivatives. 6.7 Calculation of Gibbs Derivatives Through DDs. 6.7.1 Calculation of Partial Gibbs Derivatives. References. 7 Linear Systems on Finite Non-Abelian Groups. 7.1 Linear Shift-Invariant Systems on Groups. 7.2 Linear Shift-Invariant Systems on Finite Non-Abelian Groups. 7.3 Gibbs Derivatives and Linear Systems. 7.3.1 Discussion. References. 8 Hilbert Transform on Finite Groups. 8.1 Some Results of Fourier Analysis on Finite Non-Abelian Groups. 8.2 Hilbert Transform on Finite Non-Abelian Groups. 8.3 Hilbert Transform in Finite Fields. References. Index.

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Book SynopsisNow updated in a valuable new edition, this book introduces key probability and statistical concepts through non-trivial, real-world examples and promotes the development of intuition rather than simple application.Trade Review"The book is well written and contains many interesting examples and exercises. The emphasis in these and the exposition is clearly on mathematical development and theory." (Journal of the American Statistician, December 2008) "The book is well written and contains many interesting examples and exercises. The emphasis in these and the exposition is clearly on mathematical development and theory." (Journal of the American Statistician, December 2008) "...whether you are looking for a book for classroom adoption, or just want to brush up your basic probability skills by studying on your own, you will do yourself and your students a favor by considering this book." (MAA Review March 2008)Table of ContentsPreface. 1. Experiments, Sample Spaces, and Events. 2. Probability. 3. Counting. 4. Conditional Probability; Independence. 5. Markov Chains*. 6. Random Variables: Univariate Case. 7. Random Variables: Multivariate Case. 8. Expectation. 9. Selected Families of Distributions. 10. Random Samples. 11. Introduction to Statistical Inference. 12. Estimation. 13. Testing Statistical Hypotheses. 14. Linear Models. 15. Rank Methods. 16. Analysis of Categorical Data. Statistical Tables. Bibliography. Answers to Odd-Numbered Problems. Index.

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Book SynopsisThe Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. . . . a goldmine of knowledge on accelerated life testing principles and practices . . . one of the very few capable of advancing the science of reliability. It definitely belongs in every bookshelf on engineering. Dev G. Raheja, Quality and Reliability Engineering International . . . an impressive book. The width and number of topics covered, the practical data sets included, the obvious knowledge and understanding of the author and the extent of published materials reviewed combine to ensure that this will be a book used frequently. Journal of the Royal Statistical Society A benchmark text inTrade Review"…an essential resource for an statistician involved in product development and testing...available in an attractive and reasonably priced format." (Technometrics, August 2005) "Researchers in insulation and engineers in general...will find this an outstanding reference book that will be used constantly." (IEEE Electrical Insulation Magazine, May/June 2005)Table of ContentsPreface. 1. Introduction and Background. 2. Models for Life Tests with Constant Stress. 3. Graphical Data Analysis. 4. Complete Data and Least Squares Analyses. 5. Censored Data and Maximum Likelihood Methods. 6. Test Plans. 7. Competing Failure Modes and Size Effect. 8. Least-Squares Comparisons for Complete Data. 9. Maximum Likelihood Comparisons for Censored and Other Data. 10. Models and Data Analyses for Step and Varying Stress. 11. Accelerated Degradation. Appendix A. Statistical Tables. References. Index.

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