Probability and statistics Books

Book SynopsisWinner of the 2017 De Groot Prize awarded by the International Society for Bayesian Analysis (ISBA)A relatively new area of research, adversarial risk analysis (ARA) informs decision making when there are intelligent opponents and uncertain outcomes. Adversarial Risk Analysis develops methods for allocating defensive or offensive resources against intelligent adversaries. Many examples throughout illustrate the application of the ARA approach to a variety of games and strategic situations.Focuses on the recent subfield of decision analysis, ARA Compares ideas from decision theory and game theoryUses multi-agent influence diagrams (MAIDs) throughout to help readers visualize complex information structuresApplies the ARA approach to simultaneous games, auctions, sequential games, and defend-attack gamesContains an extended case study based on a real application in railway security, whichTrade Review"This well-written and concise text is an introduction to the field of adversarial risk analysis (ARA), which is a form of decision and risk analysis which incorporates uncertainty and game theory to model strategies of an adversary…There is an appropriate amount of detail throughout the book, making it suitable for a reference text as well as a book which may be read cover to cover and it is both thought provoking and enlightening."—Matthew Craven, Plymouth University, Journal of the Royal Statistical Society, Series A, January 2017 "Here, Banks (Duke Univ.), Rios (IBM), and Insua (ICMAT-CSIC, Spain) identify three categories of uncertainty for the strategist: aleatory uncertainty—nondeterminism of outcomes even after players make choices; epistemic uncertainty—hidden information concerning opponents' preferences, beliefs, and capabilities; and concept uncertainty—hidden information concerning opponents' strategies. Adversarial risk analysis, a new field with roots in modern efforts to defeat terrorism, provides a framework, in principle, to cope with these uncertainties. Solving the models seems generally intractable, but the heart of the book, the first of its kind, offers exemplary case studies. Summing up: Recommended. Lower-division undergraduates and above; informed general audiences."—D. V. Feldman, University of New Hampshire, Durham, USA, for CHOICE, March 2016 Table of ContentsGames and Decisions. Simultaneous Games. Auctions. Sequential Games. Variations on Sequential Defend-Attack Games. A Security Case Study. Other Issues. Solutions to Selected Exercises. References. Index.

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Book SynopsisThis book provides engineers and scientists with a single source introduction to the concepts, models, and case studies for making credible reliability assessments. It satisfies the need for thorough discussions of several fundamental subjects.Section I contains a comprehensive overview of assessing and assuring reliability that is followed by discussions of: Concept of randomness and its relationship to chaos Uses and limitations of the binomial and Poisson distributions Relationship of the chi-square method and Poisson curves Derivations and applications of the exponential, Weibull, and lognormal models Examination of the human mortality bathtub curve as a template for componentsSection II introduces the case study modeling of failure data and is followed by analyses of: 5 sets of ideal Weibull, lognormal, and normal failure data 83 sets of actual (real) failure data The intent of the modeling was Table of ContentsSelected Topics. Overview of Reliability Assessments. Concept of Random. Probability & Sampling. Reliability Functions. Reliability Model: Exponential. Reliability Models: Weibull & Lognormal. Bathtub Curves for Humans & Components. Introduction & Case Studies. Introduction to Case Study Modeling of Failure Data.

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Book SynopsisPrepare Your Students for Statistical Work in the Real WorldStatistics for Engineering and the Sciences, Sixth Edition is designed for a two-semester introductory course on statistics for students majoring in engineering or any of the physical sciences. This popular text continues to teach students the basic concepts of data description and statistical inference as well as the statistical methods necessary for real-world applications. Students will understand how to collect and analyze data and think critically about the results.New to the Sixth Edition Many new and updated exercises based on contemporary engineering and scientific-related studies and real data More statistical software printouts and corresponding instructions for use that reflect the latest versions of the SAS, SPSS, and MINITAB software Introduction of the case studies at the beginning of each chapter Streamlined materiTrade Review"A salient feature of this book is the clarity with which many statistical concepts have been presented. A very nice blend of theory and applications. It contains a wealth of illustrative examples and problem sets. All the important concepts have been highlighted; real-life data has been extensively used throughout the book. Students will find it very appealing and useful on their way to learning the basic statistical concepts and tools."—Dharam V. Chopra, Wichita State University "I like the problems because they are all based on engineering applications of probability and statistics. I especially like the problems at the end of chapters because students have to think more to solve them. I favor problems that require calculations because engineers are problem solvers." —Charles H. Reilly, University of Central Florida "I think this text is one of the best I have seen when it comes down to real data sets. The authors successfully included small and large real data sets from various real-world problems in engineering, mathematical sciences, and natural sciences."—Edward J. Danial, Morgan State University Table of ContentsIntroduction. Descriptive Statistics. Probability. Discrete Random Variables. Continuous Random Variables. Bivariate Probability Distributions and Sampling Distributions. Estimation Using Confidence Intervals. Tests of Hypotheses. Categorical Data Analysis. Simple Linear Regression. Multiple Regression Analysis. Model Building. Principles of Experimental Design. The Analysis of Variance for Designed Experiments. Nonparametric Statistics. Statistical Process and Quality Control. Product and System Reliability.

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Book SynopsisDynamical Biostatistical Models presents statistical models and methods for the analysis of longitudinal data. The book focuses on models for analyzing repeated measures of quantitative and qualitative variables and events history, including survival and multistate models. Most of the advanced methods, such as multistate and joint models, can be applied using SAS or R software.The book describes advanced regression models that include the time dimension, such as mixed-effect models, survival models, multistate models, and joint models for repeated measures and time-to-event data. It also explores the possibility of unifying these models through a stochastic process point of view and introduces the dynamic approach to causal inference.Drawing on much of their own extensive research, the authors use three main examples throughout the text to illustrate epidemiological questions and methodological issues. Readers will see how each method is Trade Review"The properties of this book may be summarized in two words: rich and concise. . . this is a very well-written book that manages to cover a lot of ground in a remarkably succinct way. . . I can highly recommend the book."—Per Kragh Andersen, International Society for Clinical Biostatistics"I think that those whose research is or will be in the area of dynamical biostatistics would benefit from having a copy on their shelves."—Alice M. Richardson, Faculty of Education, Science, Technology and Mathematics, University of Canberra, Australia"This book aims at describing methods of biostatistics modeling, in particular, dynamical model approaches for statisticians, as well as serving as a textbook for postgraduate students... The balance between theory and application is appropriate for both researchers performing biostatistics modeling and for students taking graduate level courses… The book is concisely written so that it covers a wide range of basic and dynamic models and modeling approaches with examples. Statisticians in the industry may feel a large part of the book too technical but can use the book for reference and may also benefit from the rich examples and R-codes, some with translation to SAS, in the appendix." —Pharmaceutical Statistics"One of my favorite features of this book is that the same three examples are used throughout, and all the approaches discussed are applied to these examples. This allows readers to identify the similarities and differences of various techniques. Furthermore, it is a good way for readers to learn so-called data mining since diverse information can be mined by applying different statistical methods to the same dataset . . . I believe this book will be a successful text for graduate level courses focusing on dynamical biostatistical models that analyze time-dependent data. Its presentation of conventional methods is very effective."~Hongjian Zhu, Table of ContentsIntroduction. Classical Biostatistical Models: Inference. Survival Analysis. Models for Longitudinal Data. Advanced Biostatistical Models: Extensions of Mixed Models. Advanced Survival Models. Multistate Models. Joint Models for Longitudinal and Time-to-Event Data. The Dynamic Approach to Causality. Appendix: Software. Index.

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Book SynopsisUnderstand the Strategic Behavior in Queueing SystemsRational Queueing provides one of the first unified accounts of the dynamic aspects involved in the strategic behavior in queues. It explores the performance of queueing systems where multiple agents, such as customers, servers, and central managers, all act but often in a noncooperative manner.The book first addresses observable queues and models that assume state-dependent behavior. It then discusses other types of information in queueing systems and compares observable and unobservable variations and incentives for information disclosure. The next several chapters present relevant models for the maximization of individual utilities, social welfare, and profits. After covering queueing networks, from simple parallel servers to general network structures, the author describes models for planned vacations and forced vacations (such as breakdowns). Focusing on supply chaiTrade Review"This unique bibliographical volume by a foremost researcher in the area of strategic queues, or game theoretical analysis of queueing systems, provides a complete panorama of the extensive literature that was published in this area in recent years, spanning the period since the by-now classical monograph of Hassin and Haviv (2003) up to the present day. With over 700 references, individual papers are typically summarized in a paragraph or two, highlighting their essential contribution. The surveyed articles are arranged within a thoughtful subject classification, which makes it easy to focus on topics of interest, while the chronological ordering within each subject clearly displays the progression of ideas and results. Anyone who works in the area of strategic queues should have this book handy on his or her bookshelf. A newcomer may first study the above-mentioned monograph and come back to the present book to fully realize the state of the art."- Nahum Shimkin, Professor of Electrical Engineering, Technion"Rational Queueing provides a comprehensive and authoritative survey of recent research on strategic behavior in queueing systems. Focusing on advances in the field since the publication of the classic To Queue or Not to Queue, the author brings the reader up to date by summarizing and organizing over 700 papers from multiple disciplines in a unifying framework. This book will serve as an indispensable reference for researchers, students, and teachers in this area."- Philipp Afèche, Associate Professor of Operations Management, Rotman School of Management, University of Toronto"Rational Queueing is the book that defines and summarizes the important area of operations research that combines queueing with game theory. This is a must-have reference for anyone that is interested in game-theoretic considerations in queueing models. It will be immensely useful as an introduction for beginners and as a reference for mature researchers in the area. Professor Hassin has done a superb job. The book can be used for independent study, but also as the main source for graduate seminars on production, service, and operations management."- Antonis Economou, Department of Mathematics, University of Athens"This really is a must read for researchers in game theory, from those just starting out in this field through to more established researchers. It is also a valuable teaching resource, covering both undergraduate topics through to a comprehensive and state-of-the-art review of modern trends in the subject for postgraduate students."- Paul Harper, Professor of Operational Research and Deputy Head of School of Mathematics, Cardiff University"With the gross domestic product (GDP) in the service sector accounting for over 90 percent of the whole GDP in many countries and areas such as the United States and Hong Kong, service management is becoming increasingly important. Different from a manufacturing system, a service system has direct contact with customers, a feature that has inspired an increasing trend on studying service management with strategic customers. This book provides a timely and inclusive summary of studies on strategic customer behavior and games among service providers in recent years. I was amazed by two main features of the book. One, the number of papers surveyed is enormous. With over 700 papers surveyed, the book covers a wide range of topics on games among customers and games among service providers. In particular, it surveys those cutting-edge topics in the field such as bounded-rationality and loss-aversion customer behavior. Two, the reviews on papers are extremely accurate. I heard from many researchers that the author of the book, Prof. Refael Hassin, contacted them individually, asking for feedback on the review of their work. I was also requested to provide comments on my work during the writing of this book. These steps assure the high quality of the book. This book can serve as an excellent reference book for researchers and graduate students in the fields of operations management, operations research, industry engineering, civil engineering, and computer science. This is a must-have book and is greatly helpful and handy for researchers in fields involving strategic customers."- Dr. Pengfei Guo, Associate Professor and Associate Head, Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University"In this book, the author gives an extensive survey on queueing systems in which the agents interact to maximize certain goals. The book is a follow-up of a book on strategic queueing co-authored by the author and M. Haviv [To queue or not to queue: equilibrium behavior in queueing systems, Internat. Ser. Oper. Res. Management Sci., 59, Kluwer Acad. Publ., Boston, MA, 2003; MR2006433]. [..] This book is excellent reading for any researcher interested in the state of the art of rational queueing. It provides an overview on recent work combining queueing systems and game theory."- Judith Timmer, Mathematical Reviews, January 2017"This unique bibliographical volume by a foremost researcher in the area of strategic queues, or game theoretical analysis of queueing systems, provides a complete panorama of the extensive literature that was published in this area in recent years, spanning the period since the by-now classical monograph of Hassin and Haviv (2003) up to the present day. With over 700 references, individual papers are typically summarized in a paragraph or two, highlighting their essential contribution. The surveyed articles are arranged within a thoughtful subject classification, which makes it easy to focus on topics of interest, while the chronological ordering within each subject clearly displays the progression of ideas and results. Anyone who works in the area of strategic queues should have this book handy on his or her bookshelf. A newcomer may first study the above-mentioned monograph and come back to the present book to fully realize the state of the art."- Nahum Shimkin, Professor of Electrical Engineering, Technion"Rational Queueing provides a comprehensive and authoritative survey of recent research on strategic behavior in queueing systems. Focusing on advances in the field since the publication of the classic To Queue or Not to Queue, the author brings the reader up to date by summarizing and organizing over 700 papers from multiple disciplines in a unifying framework. This book will serve as an indispensable reference for researchers, students, and teachers in this area."- Philipp Afèche, Associate Professor of Operations Management, Rotman School of Management, University of Toronto"Rational Queueing is the book that defines and summarizes the important area of operations research that combines queueing with game theory. This is a must-have reference for anyone that is interested in game-theoretic considerations in queueing models. It will be immensely useful as an introduction for beginners and as a reference for mature researchers in the area. Professor Hassin has done a superb job. The book can be used for independent study, but also as the main source for graduate seminars on production, service, and operations management."- Antonis Economou, Department of Mathematics, University of Athens"This really is a must read for researchers in game theory, from those just starting out in this field through to more established researchers. It is also a valuable teaching resource, covering both undergraduate topics through to a comprehensive and state-of-the-art review of modern trends in the subject for postgraduate students."- Paul Harper, Professor of Operational Research and Deputy Head of School of Mathematics, Cardiff University"With the gross domestic product (GDP) in the service sector accounting for over 90 percent of the whole GDP in many countries and areas such as the United States and Hong Kong, service management is becoming increasingly important. Different from a manufacturing system, a service system has direct contact with customers, a feature that has inspired an increasing trend on studying service management with strategic customers. This book provides a timely and inclusive summary of studies on strategic customer behavior and games among service providers in recent years. I was amazed by two main features of the book. One, the number of papers surveyed is enormous. With over 700 papers surveyed, the book covers a wide range of topics on games among customers and games among service providers. In particular, it surveys those cutting-edge topics in the field such as bounded-rationality and loss-aversion customer behavior. Two, the reviews on papers are extremely accurate. I heard from many researchers that the author of the book, Prof. Refael Hassin, contacted them individually, asking for feedback on the review of their work. I was also requested to provide comments on my work during the writing of this book. These steps assure the high quality of the book. This book can serve as an excellent reference book for researchers and graduate students in the fields of operations management, operations research, industry engineering, civil engineering, and computer science. This is a must-have book and is greatly helpful and handy for researchers in fields involving strategic customers."- Dr. Pengfei Guo, Associate Professor and Associate Head, Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University"The book summarizes a big amount of actual results concerning the combination of queueing theory and game theory. It indicates the results of over 700 papers appearing in the bibliography in this area and very accurately refers their contents reecting the most actual achievements in a wide range of topics on games among customers and service providers. It can highly be recommended to researchers, teachers and students working in this area, even one can say it is an indispensable handbook for them."- L□aszl□o Lakatos (Budapest)"In this book, the author gives an extensive survey on queueing systems in which the agents interact to maximize certain goals. The book is a follow-up of a book on strategic queueing co-authored by the author and M. Haviv [To queue or not to queue: equilibrium behavior in queueing systems, Internat. Ser. Oper. Res. Management Sci., 59, Kluwer Acad. Publ., Boston, MA, 2003; MR2006433]. [..] This book is excellent reading for any researcher interested in the state of the art of rational queueing. It provides an overview on recent work combining queueing systems and game theory."- Judith Timmer, Mathematical Reviews, January 2017Table of ContentsIntroduction. Observable queues. Information. Customer decisions. Social optimization and cooperation. Monopoly. Competition. Routing in queueing networks. Supply chains, outsourcing, and contracting. Vacations. Bounded rationality. Bibliography. Indices.

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Book SynopsisA properly structured financial model can provide decision makers with a powerful planning tool that helps them identify the consequences of their decisions before they are put into practice. Introduction to Financial Models for Management and Planning, Second Edition enables professionals and students to learn how to develop and use computer-based models for financial planning. This volume provides critical tools for the financial toolbox, then shows how to use them tools to build successful models.Table of ContentsAn Overview of Financial Planning and Modeling. Part I: Tools for Financial Planning and Modeling: Financial Analysis. The Tools for Financial Planning I: Financial Analysis. Appendix A: Using Names in the Excel Spreadsheet. Appendix B: Constructing a Data Table. The Tools for Financial Planning II: Growth and Cash Flows. Part II: Tools for Financial Planning and Modeling: Simulation. Financial Statement Simulation. Monte Carlo Simulation. Part III: Introduction to Forecasting Methods. Forecasting I: Time Trend Extrapolation. Forecasting II: Econometric Forecasting. Forecasting III: Smoothing Data for Forecasts. Part IV: A Closer Look at the Details of a Financial Model. Modeling Value. Modeling Long-Term Assets. Debt Financing. Modeling Working Capital Accounts. PART V: Modeling Security Prices and Investment Portfolios. Modeling Security Prices. Constructing Optimal Security Portfolios. Options. Part VI: Optimization Models. Optimization Models for Financial Planning. Planning and Managing Working Capital with LP. References. Index

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Book SynopsisPraise for the first edition:Given the author's years of experience as a statistician and as a founder of the first DMC in pharmaceutical industry trials, I highly recommend this booknot only for experts because of its cogent and organized presentation, but more importantly for young investigators who are seeking information about the logistical and philosophical aspects of a DMC. -S. T. Ounpraseuth, The American Statistician In the first edition of this well-regarded book, the author provided a groundbreaking and definitive guide to best practices in pharmaceutical industry data monitoring committees (DMCs). Maintaining all the material from the first edition and adding substantial new material, Data and Safety Monitoring Committees in Clinical Trials, Second Edition is ideal for training professionals to serve on their first DMC as well as for experienced clinical and biostatistical DMC members, sponsor and regTrade Review "The book by Dr. Herson is written amazingly well. The book concentrates on pharmaceutical industrysponsored confirmatory clinical trials and can serve as excellent sources of knowledge for all the aspects of data safety monitoring committee (DMC) activities. A great feature of the book is the “DMCounselor” section at the end of each chapter, covering nearly 70 questions with answers, of which about 33% are for a DMC Chair, 30% for the DMC Biostatistician member, 30% for a DMC physician member, and the rest are for others (e.g., project manager)."~ Daniel Jia, Journal of Biopharmaceutical Statistics"Nicely written and readable cover-to-cover, the author walks through every facet of a Data Monitoring Committee (DMC) beginning with an overview of their past and current place in drug development, to how they are organized and interfaced with other committees, and on to the specifics of how a typical meeting is split into an open and closed session. From there it moves on to clinical issues, including how SAEs are categorized, statistical methods, including Bayesian and frequentist conditional power calculations, common biases and pitfalls, and guidance for how DMC decisions are made. It concludes with emerging issues due to new clinical trial designs mandated by the FDA to speed up the drug development process."~Donna Pauler Ankerst, BiometricsTable of ContentsPreface to the Second Edition. Introduction. Organization of a Safety Monitoring Program for a Confirmatory Trial. Meetings. Clinical Issues. Statistical Issues. Biases and Pitfalls. DMC Decisions. Emerging issues. Appendix.

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Book SynopsisThis would be an excellent book for undergraduate, graduate and beyond.The style of writing is easy to read and the author does a good job of adding humor in places. The integration of basic programming in R with the data that is collected for any experiment provides a powerful platform for analysis of data. having the understanding of data analysis that this book offers will really help researchers examine their data and consider its value from multiple perspectives and this applies to people who have small AND large data sets alike! This book also helps people use a free and basic software system for processing and plotting simple to complex functions. Michelle Pantoya, Texas Tech UniversityMeasurements of quantities that vary in a continuous fashion, e.g., the pressure of a gas, cannot be measured exactly and there will always be some uncertainty with these measured values, so it is vital for researchers to be able to quantify this data. UncertaTable of ContentsTABLE OF CONTENTS CHAPTER 1 INTRODUCTION * What Is This Book About? *Units *Physical Constants and Their Uncertainties *Dimensionless Quantities *Software *Topics Covered *References *Problems *CHAPTER 2 ASPECTS OF R * Getting R *Using R *Getting Help *Libraries and Packages *Variables *Vectors *Arithmetic *Data Frames *Exporting Data *Importing Data *Internal Mathematical Functions *Writing Your Own Functions *Plotting Mathematical Functions *Loops *Making Decisions *Scripts *Reading Data from Websites *Matrices and Linear Algebra *Some Useful Functions and Operations *Data Frames *Vectors *Probability and Statistics *Plotting *Matrices and Linear Algebra *Data/Functions/Libraries/Packages *Various *References *Problems *CHAPTER 3 STATISTICS * Populations and Samples *Mean, Median, Standard Deviation, and Variance of a Sample *Covariance and Correlation *Visualizing Data *Histograms *Box Plots *Plotting Data Sets *Some Plotting Parameters and Commands *Estimating Population Statistics *Confidence Interval for the Population Mean Using Student's t Variables *Confidence Interval for the Population Variance Using Chi-Square Variables *Confidence Interval Interpretation *Comparing the Means of Two Samples *Testing Data for Normality *Outlier Identification *Modified Thompson Technique *Chauvenet's Criterion *References *Problems *CHAPTER 4 CURVE FITS * Linear Regression *Nonlinear Regression *Kernel Smoothing *References *Problems *CHAPTER 5 UNCERTAINTY OF A MEASURED QUANTITY * What Is Uncertainty? *Random Variables *Measurement Uncertainties *Elemental Systematic Errors *Normal Distributions *Uniform Distributions *Triangular Distributions *Coverage Factors *References *Problems *CHAPTER 6 UNCERTAINTY OF A RESULT CALCULATED USING EXPERIMENTAL DATA * Taylor Series Approach *Coverage Factors *The Kline-McClintock Equation *Balance Checks *References *Problems *CHAPTER 7 TAYLOR SERIES UNCERTAINTY OF A LINEAR REGRESSION CURVE FIT…………………………………………………………………………………………. * Curve-fit Expressions………………………………………………………………………. *Cases to Consider…………………………………………………………………………... *Case 1: No Errors and No Correlations *Case 2: Random Errors Only *Case 3: Random and Systematic Errors *General Linear Regression Theory *Uncertainties in Regression Coefficients *Evaluating Uncertainties with Built-in R functions *References *Problems *CHAPTER 8 MONTE CARLO METHODS * Overall Monte Carlo Approach *Random Number Generation *Accept/Reject Method *Inverse-cdf Method *Random Sampling *Uncertainty of a Measured Variable *Bootstrapping with Internal Functions in R *Monte Carlo Convergence Criteria *Uncertainty of a Result Calculated Using Experimental Data *Uncertainty Bands for Linear Regression Curve Fits *Uncertainty Bands for a Curve Fit with Kernel Smoothing *References *Problems *CHAPTER 9 THE BAYESIAN APPROACH * Bayes Theorem for Probability Density Functions *Bayesian Estimation of the Mean and Standard Deviation of a Normal Population *References *Problems *APPENDIX PROBABILITY DENSITY FUNCTIONS * Univariate pdfs *Normal Distribution *Uniform Distribution *Triangular Distribution *Student's t Distribution *Chi-Square Distribution *Multivariate pdfs *Marginal Distributions *References *

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Book SynopsisExam board: Cambridge Assessment International EducationLevel: A-levelSubject: MathematicsFirst teaching: September 2018First exams: Summer 2020Endorsed by Cambridge Assessment International Education to provide full support for Paper 4 of the syllabus for examination from 2020.Take mathematical understanding to the next level with this accessible series, written by experienced authors, examiners and teachers.- Improve confidence as a mathematician with clear explanations, worked examples, diverse activities and engaging discussion points. - Advance problem-solving, interpretation and communication skills through a wealth of questions that promote higher-order thinking. - Prepare for further study or life beyond the classroom by applying mathematics to other subjects and modelling real-world situations.- Reinforce learning with opportunities for digital practice via links to the Mathematics in Education and Industry's (MEI) Integral platform in the eBooks.**To have full access to the eBooks and Integral resources you must be subscribed to both Boost and Integral. To trial our eBooks and/or subscribe to Boost, visit: www.hoddereducation.co.uk/boost; to view samples of the Integral resources and/or subscribe to Integral, visit integralmaths.org/internationalPlease note that the Integral resources have not been through the Cambridge International endorsement process. Answers to exercise questions are on Cambridge Extras: www.hoddereducation.co.uk/cambridgeextrasThis book covers the syllabus content for Further Probability and Statistics, including continuous random variables, inference using normal and t-distributions, chi-squared tests, non-parametric tests and probability generating functions.

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Book SynopsisExam board: Cambridge Assessment International EducationLevel: A LevelSubject: MathematicsFirst teaching: September 2018First exams: Summer 2020Reinforce learning and deepen understanding of the key concepts covered in the latest syllabus; an ideal course companion or homework book for use throughout the course.- Develop and strengthen skills and knowledge with a wealth of additional exercises that perfectly supplement the Student's Book. - Build confidence with extra practice for each lesson to ensure that a topic is thoroughly understood before moving on. - Ensure students know what to expect with hundreds of rigorous practice and exam-style questions. - Keep track of students' work with ready-to-go write-in exercises. - Save time with all answers available for free online: www.hoddereducation.co.uk/cambridgeextras.This book covers the syllabus content for Probability and Statistics 2, including the Poisson distribution, linear combinations of random variables, continuous random variables, sampling and estimation and hypothesis tests. This title has not been through the Cambridge Assessment International Education endorsement process.Available in this series:Five textbooks fully covering the latest Cambridge International AS & A Level Mathematics syllabus (9709) are accompanied by a Workbook, and Student and Whiteboard eTextbooks.Pure Mathematics 1: Student Textbook (ISBN 9781510421721), Student eTextbook (ISBN 9781510420762), Whiteboard eTextbook (ISBN 9781510420779), Workbook (ISBN 9781510421844)Pure Mathematics 2 and 3: Student Textbook (ISBN 9781510421738), Student eTextbook (ISBN 9781510420854), Whiteboard eTextbook (ISBN 9781510420878), Workbook (ISBN 9781510421851)Mechanics: Student Textbook (ISBN 9781510421745), Student eTextbook (ISBN 9781510420953), Whiteboard eTextbook (ISBN 9781510420977), Workbook (ISBN 9781510421837)Probability & Statistics 1: Student Textbook (ISBN 9781510421752), Student eTextbook (ISBN 9781510421066), Whiteboard eTextbook (ISBN 9781510421097), Workbook (ISBN 9781510421875)Probability & Statistics 2: Student Textbook (ISBN 9781510421776), Student eTextbook (ISBN 9781510421158), Whiteboard eTextbook (ISBN 9781510421165), Workbook (9781510421882)

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Book SynopsisBreaking through the World of Statistics introduces students to statistics and processes that organize, summarize, and apply data to authentic situations. Instruction within the text is based on the principle of learning-by-doing. Each chapter first presents a specific theory or process for problem-solving, and then applies that theory or process to real-world problems.The content features information drawn from diverse disciplines including business and sports. Over the course of the text, students will learn about statistics and their measurement, data organization, descriptive statistics, and probability, both discrete and continuous. They will also study sampling and sampling distributions, confidence intervals, hypothesis testing, analysis of the variance, and both simple and multiple linear regression.The book has been developed to demonstrate that statistics is not a single discipline, but rather has broad applications for numerous areas of life and work. Breaking through the World of Statistics is designed for introductory statistics courses and to successfully prepare students for intermediate-level study.

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Book SynopsisProbability plays an essential role in making decisions in areas such as business, politics, and sports, among others. Professor Rabinowitz, based on many years of teaching, has created a textbook suited for classroom use as well as for self-study that is filled with hundreds of carefully chosen examples based on real-world case studies about sports, elections, drug testing, legal cases, population growth, business, and more. His approach is innovative, practical, and entertaining. Elementary Probability with Applications will serve to enhance classroom instruction, as well as benefit those who want to review the basics of probability at their own pace. The text is used at several colleges and for some high school classes.Trade Review" ""The chosen approach is practical and entertaining. The book is a useful tool for teachers and for anybody interested in basic ideas and applications of classical probability theory."" -EMS Newsletter, June 2005 ""This book would be excellent for a minicourse at a higher level of high school as well as a semester course at the college level."" -Larry White, NCTM, October 2005 ""This book was surprisingly refreshing and did a great job using real situations to motivate techniques for calculating discrete probabilities. . ."" -Technometrics, August 2006 ""This is a very elementary book on probability which has the merits of clear exposition and ... a host of interesting applications, not just the balls-in-urns variety, but to machine reliability, juries, cryptography, birth control, airline management, and sport."" -D.V. Lindley, The Mathematical Gazette, November 2006 ""This book is one of the most elementary introductions to probability available."" -Nieuw Archief voor Wiskunde, March 2008 The writing style is quite pleasant, and many interesting examples are given. These applications are, in my opinion, the most interesting part of the book, and include the usual examples from card and other games, but also examples like the frequency of letters in English or detection of drug users. -R. Van Der Hofstad, Nieuw Archief voor Wiskunde, March 2008"Table of ContentsBasic Concepts in Probability Sample Spaces, Events, and Probabilities Simulations Complementary Events and Mutually Exclusive Events Some Probability Rules Problem Solving Problems Conditional Probability and the Multiplication Rule Conditional Probability Multiplication Rule Problems Independence Independence A Technique for Finding P(A or B or C or ...) Problems Combining the Addition and Multiplication Rules Combining the Addition and Multiplication Rules Bayes' Formula Trees Problems Combining the Addition and Multiplication Rules-Applications Simpson's Paradox Randomized Response Designs Applications in Cryptology Hardy-Weinberg Principle Problems Random Variables, Distributions, and Expected Values Random Variables, Distributions, and Expected Values Problems Joint Distributions and Conditional Expectations Joint Distributions Independent Random Variables Conditional Distributions Conditional Expectations Problems Sampling without Replacement Counting Formula Probabilities for Sampling without Replacement Problems Sampling with Replacement Binomial Model Problems Sampling with Replacement (Continued) Binomial Model (Continued) Problems Binomial Tests Introduction Binomial Tests Problems Appendix Short Answers to Selected Exercises Bibliography Index

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Book SynopsisIn the view of many probabilists, author Anatolii Puhalskii's research results stand among the most significant achievements in the modern theory of large deviations. In fact, his work marked a turning point in the depth of our understanding of the connections between the large deviation principle (LDP) and well-known methods for establishing weak convergence results.Large Deviations and Idempotent Probability expounds upon the recent methodology of building large deviation theory along the lines of weak convergence theory. The author develops an idempotent (or maxitive) probability theory, introduces idempotent analogues of martingales (maxingales), Wiener and Poisson processes, and Ito differential equations, and studies their properties. The large deviation principle for stochastic processes is formulated as a certain type of convergence of stochastic processes to idempotent processes. The author calls this large deviation convergence.The approach to establishing large deviation convergence uses novel compactness arguments. Coupled with the power of stochastic calculus, this leads to very general results on large deviation asymptotics of semimartingales. Large and moderate deviation asymptotics are treated in a unified manner. Starting with the foundations of idempotent measure theory and culminating in applications to large deviation asymptotics of queueing systems, Large Deviations and Idempotent Probability offers an outstanding opportunity to examine both the development of a remarkable approach and recently discovered results as presented by one of the foremost leaders in the field.Table of ContentsIDEMPOTENT PROBABILITY THEORY: Idempotent Probability Measures. Maxingales. LARGE DEVIATION CONVERGENCE: Large Deviation Convergence in Tihonov Spaces. The Method of Finite-Dimensional Distributions. The Method of the Maxingale Problem. APPLICATIONS.

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Book SynopsisThis volume discusses an important area of statistics and highlights the most important statistical advances. It is divided into four sections: statistics in the life and medical sciences, business and social science, the physical sciences and engineering, and theory and methods of statistics.Trade Review"This impressive volume is highly recommended for all statisticians as well as anybody who is interested in applying statistics in any science."- Perceptual and Motor Skills, December 2001 "Even though statistics is used in different disciplines in different contexts, this volume reveals an underlying cohesiveness of the field. With the growth of computer power and storage, researchers are analyzing large and complex data sets, leading to the need for new methods of model selection. Material is presented clearly and informatively. Extensive author and subject indexes. A valuable addition to academic libraries."--CHOICE Magazine, May 2002Table of ContentsIntroduction. Statistics in the Life and Medical Sciences. Statistics in Business and Social Science. Statistics in the Physical Sciences and Engineering. Theory and Methods. Author Index. Subject Index.

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Book SynopsisExamines Critical Decisions for Transitioning Lab Science to a Clinical SettingThe development of therapeutic pharmaceutical compounds is becoming more expensive, and the success rates for getting such treatments approved for marketing and to the patients is decreasing. As a result, translational medicine (TM) is becoming increasingly important in the healthcare industry – a means of maximizing the consideration and use of information collected as compounds transition from initial lab discovery, through pre-clinical testing, early clinical trials, and late confirmatory studies that lead to regulatory approval of drug release to patients. Translational Medicine: Strategies and Statistical Methods suggests a process for transitioning from the initial lab discovery to the patient’s bedside with minimal disconnect and offers a comprehensive review of statistical design and methodology commonly employed in this bench-to-bedside research. Documents Alternative Research Approaches for Faster and More Accurate Data Judgment CallsElaborating on how to introduce TM into clinical studies, this authoritative work presents a keen approach to building, executing, and validating statistical models that consider data from various phases of development. It also delineates a truly translational example to help bolster understanding of discussed concepts. This comprehensive guide effectively demonstrates how to overcome obstacles related to successful TM practice. It contains invaluable information for pharmaceutical scientists, research executives, clinicians, and biostatisticians looking to expedite successful implementation of this important process.Trade Review"This is one of the few books published on the strategies for TM. The chapters are carefully coordinated and can be read on their own; they are independent but are still well coordinated. The book contains a good outline of the different aspects of TM and contains a series of good examples. ... this book will provide interesting reading for readers from a variety of backgrounds. Overall, this book contains a good foundation for anyone working in this area." -Richardus Vonk, Pharmaceutical Statistics "... chapters follow the natural order from discovery research to final implementation to intermediate validation." -Erik Cobo, International Society for Clinical BiostatisticsTable of ContentsTranslational Medicine: Strategies and Statistical Methods. Strategic Concepts in Translational Medicine. Design and Analysis Approaches for Discovery Translational Medicine. Biomarker Development. Targeted Clinical Trials. Statistical Methods in Translational Medicine. NonparametricMethods in Translational Research. Model Selection/Validation. Translation in Clinical Information between Populations—Bridging Studies. Translation in Clinical Technology—Traditional Chinese Medicine. Index.

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Book SynopsisBayesian Analysis with Stata is written for anyone interested in applying Bayesian methods to real data easily. The book shows how modern analyses based on Markov chain Monte Carlo (MCMC) methods are implemented in Stata both directly and by passing Stata datasets to OpenBUGS or WinBUGS for computation, allowing Stata’s data management and graphing capability to be used with OpenBUGS/WinBUGS speed and reliability.The book emphasizes practical data analysis from the Bayesian perspective, and hence covers the selection of realistic priors, computational efficiency and speed, the assessment of convergence, the evaluation of models, and the presentation of the results. Every topic is illustrated in detail using real-life examples, mostly drawn from medical research.The book takes great care in introducing concepts and coding tools incrementally so that there are no steep patches or discontinuities in the learning curve. The book's content helps the user see exactly what computations are done for simple standard models and shows the user how those computations are implemented. Understanding these concepts is important for users because Bayesian analysis lends itself to custom or very complex models, and users must be able to code these themselves.Trade Review"… the first comprehensive guide to employing Bayesian methods using Stata statistical software. … until this book, there has been no unified presentation of how to implement Bayesian methods using Stata. … A nice feature of the book is the use of real data … I recommend it for Stata users who wish to employ Bayesian modeling within the Stata environment."—International Statistical Review, 2015Table of ContentsList of figures. List of tables. Preface. Acknowledgments. The problem of priors. Evaluating the posterior. Metropolis–Hastings. Gibbs sampling. Assessing convergence. Validating the Stata code and summarizing the results. Using WinBUGS for model fitting. Model checking. Model selection. Further case studies. Writing Stata programs for specific Bayesian analysis. A Standard distributions. References . Author index . Subject index.

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Book SynopsisOne Hundred Nineteen Stata Tips provides concise and insightful notes about commands, features, and tricks that will help you obtain a deeper understanding of Stata. The book comprises the contributions of the Stata community that have appeared in the Stata Journal since 2003.Table of ContentsIntroducing Stata tips. Stata tip 1: The eform() option of regress. Stata tip 2: Building with floors and ceilings. Stata tip 3: How to be assertive. Stata tip 4: Using display as an online calculator. Stata tip 5: Ensuring programs preserve dataset sort order. Stata tip 6: Inserting awkward characters in the plot. Stata tip 7: Copying and pasting under Windows. Stata tip 8: Splitting time-span records with categorical time-varying covariates. Stata tip 9: Following special sequences. Stata tip 10: Fine control of axis title positions. Stata tip 11: The nolog option with maximum-likelihood modeling commands. Stata tip 12: Tuning the plot region aspect ratio. Stata tip 13: generate and replace use the current sort order. Stata tip 14: Using value labels in expressions. Stata tip 15: Function graphs on the fly. Stata tip 16: Using input to generate variables. Stata tip 17: Filling in the gaps. Stata tip 18: Making keys functional. Stata tip 19: A way to leaner, faster graphs. Stata tip 20: Generating histogram bin variables. Stata tip 21: The arrows of outrageous fortune. Stata tip 22: Variable name abbreviation. Stata tip 23: Regaining control over axis ranges. Stata tip 24: Axis labels on two or more levels. Stata tip 25: Sequence index plots. Stata tip 26: Maximizing compatibility between Macintosh and Windows. Stata tip 27: Classifying data points on scatter plots. Stata tip 28: Precise control of dataset sort order. Stata tip 29: For all times and all places. Stata tip 30: May the source be with you. Stata tip 31: Scalar or variable? The problem of ambiguous names. Stata tip 32: Do not stop. Stata tip 33: Sweet sixteen: Hexadecimal formats and precision problems. Stata tip 34: Tabulation by listing. Stata tip 35: Detecting whether data have changed. Stata tip 36: Which observations? Stata tip 37: And the last shall be first. Stata tip 38: Testing for groupwise heteroskedasticity. Stata tip 39: In a list or out? In a range or out? Stata tip 40: Taking care of business. Stata tip 41: Monitoring loop iterations. Stata tip 42: The overlay problem: Offset for clarity. Stata tip 43: Remainders, selections, sequences, extractions: Uses of the modulus. Stata tip 44: Get a handle on your sample. Stata tip 45: Getting those data into shape. Stata tip 46: Step we gaily, on we go. Stata tip 47: Quantile–quantile plots without programming. Stata tip 48: Discrete uses for uniform(). Stata tip 49: Range frame plots. Stata tip 50: Efficient use of summarize. Stata tip 51: Events in intervals. Stata tip 52: Generating composite categorical variables. Stata tip 53: Where did my p-values go? Stata tip 54: Post your results. Stata tip 55: Better axis labeling for time points and time intervals. Stata tip 56: Writing parameterized text files. Stata tip 57: How to reinstall Stata. Stata tip 58: nl is not just for nonlinear models. Stata tip 59: Plotting on any transformed scale. Stata tip 60: Making fast and easy changes to files with filefilter. Stata tip 61: Decimal commas in results output and data input. Stata tip 62: Plotting on reversed scales. Stata tip 63: Modeling proportions. Stata tip 64: Cleaning up user-entered string variables. Stata tip 65: Beware the backstabbing backslash. Stata tip 66: ds—A hidden gem. Stata tip 67: J() now has greater replicating powers. Stata tip 68: Week assumptions. Stata tip 69: Producing log files based on successful interactive commands. Stata tip 70: Beware the evaluating equal sign. Stata tip 71: The problem of split identity, or how to group dyads. Stata tip 72: Using the Graph Recorder to create a pseudograph scheme. Stata tip 73: append with care! Stata tip 74: firstonly, a new option for tab2. Stata tip 75: Setting up Stata for a presentation. Stata tip 76: Separating seasonal time series. Stata tip 77: (Re)using macros in multiple do-files. Stata tip 78: Going gray gracefully: Highlighting subsets and downplaying substrates. Stata tip 79: Optional arguments to options. Stata tip 80: Constructing a group variable with specified group sizes. Stata tip 81: A table of graphs. Stata tip 82: Grounds for grids on graphs. Stata tip 83: Merging multilingual datasets. Stata tip 84: Summing missings. Stata tip 85: Looping over nonintegers. Stata tip 86: The missing() function. Stata tip 87: Interpretation of interactions in nonlinear models. Stata tip 88: Efficiently evaluating elasticities with the margins command. Stata tip 89: Estimating means and percentiles following multiple imputation. Stata tip 90: Displaying partial results. Stata tip 91: Putting unabbreviated varlists into local macros. Stata tip 92: Manual implementation of permutations and bootstraps. Stata tip 93: Handling multiple y axes on twoway graphs. Stata tip 94: Manipulation of prediction parameters for parametric survival regression. Stata tip 95: Estimation of error covariances in a linear model. Stata tip 96: Cube roots. Stata tip 97: Getting at ρ’s and σ’s. Stata tip 98: Counting substrings within strings. Stata tip 99: Taking extra care with encode. Stata tip 100: Mata and the case of the missing macros. Stata tip 101: Previous but different. Stata tip 102: Highlighting specific bars. Stata tip 103: Expressing confidence with gradations. Stata tip 104: Added text and title options. Stata tip 105: Daily dates with missing days. Stata tip 106: With or without reference. Stata tip 107: The baseline is now reported. Stata tip 108: On adding and constraining. Stata tip 109: How to combine variables with missing values. Stata tip 110: How to get the optimal k-means cluster solution. Stata tip 111: More on working with weeks. Stata tip 112: Where did my p-values go? (Part 2) Stata tip 113: Changing a variable’s format: What it does and does not mean. Stata tip 114: Expand paired dates to pairs of dates. Stata tip 115: How to properly estimate the multinomial probit model with heteroskedastic errors. Stata tip 116: Where did my p-values go? (Part 3). Stata tip 117: graph combine—Combining graphs. Stata tip 118: Orthogonalizing powered and product terms using residual centering. Stata tip 119: Expanding datasets for graphical ends.

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Book SynopsisMeta-analysis allows researchers to combine the results of several studies into a unified analysis that provides an overall estimate of the effect of interest. This collection of articles from the Stata Journal and Stata Technical Bulletin will be indispensable to researchers who wish to conduct meta-analyses using Stata and learn about the full range of user-written Stata meta-analysis commands. With these articles and the associated Stata software, you gain access to the statistical methods behind the rapid increase in the number of meta-analyses reported in the social and medical literature.Collectively, the articles provide a detailed description of a range of meta-analytic methods. They show how to conduct and interpret meta-analyses; how to produce highly flexible graphical displays; how to use meta-regression; how to examine bias; how to conduct individual participant data meta-analysis; and how to conduct multivariate meta-analysis. This edition also contains three articles on network metaanalysis, a major recent development in meta-analysis methodology.Table of ContentsMeta-analysis in Stata: metan, metaan, metacum, and metap. Meta-regression: metareg. Investigating bias in meta-analysis: metafunnel, confunnel, metabias, metatrim, and extfunnel. Multivariate meta-analysis: metandi, mvmeta. Network meta-analysis: indirect, network package, network graphs package.

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Book SynopsisThis volume is a sometimes serious and sometimes whimsical retrospective of Stata, its development, and its use over the last 30 years.The view from the inside opens with an essay by Bill Gould, Stata's president and cofounder, that discusses the challenges and concepts that guided the design and implementation of Stata. This is followed by an interview of Bill by Joe Newton that discusses Bill's early interest in computing, his early work on a program for matching prom dates in the days when you had to purchase time on computers, and further exploration of the guiding principles behind Stata. Finally, Sean Becketti, Stata's first employee, delves into the not-to-be-missed culture of Stata in its infancy.The view from the outside comprises 14 essays by prominent researchers and members of the Stata community. Most discuss Stata's use and evolution in disciplines such as behavioral sciences, business, economics, epidemiology, time series, political science, public health, public policy, veterinary epidemiology, and statistics. Some take a sweeping overview. Others are more intimate personal recollections. Mostly, we simply wanted to celebrate the relationship between Stata users and Stata software. We hope that this volume holds something interesting for everyone.Table of ContentsA VISION FROM INSIDE. Initial thoughts. A conversation with William Gould. A VISION FROM OUTSIDE. Then and now. 25 years of Statistics with Stata. Stata’s contribution to epidemiology. The evolution of veterinary epidemiology. On learning introductory biostatistics and Stata. Stata and public health in Ohio. Statistics research and Stata in my life. Public policy and Stata. Microeconometrics and Stata over the past 30 years. Stata enabling state-of-the-art research in accounting, business, and finance. Stata and political science. New tools for psychological researchers. History of Stata.

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Book SynopsisHealth Econometrics Using Stata by Partha Deb, Edward C. Norton, and Willard G. Manning provides an excellent overview of the methods used to analyze data on healthcare expenditure and use. Aimed at researchers, graduate students, and practitioners, this book introduces readers to widely used methods, shows them how to perform these methods in Stata, and illustrates how to interpret the results. Each method is discussed in the context of an example using an extract from the Medical Expenditure Panel Survey.After the overview chapters, the book provides excellent introductions to a series of topics aimed specifically at those analyzing healthcare expenditure and use data. The basic topics of linear regression, the generalized linear model, and log and Box-Cox models are covered with a tight focus on the problems presented by these data. Using this foundation, the authors cover the more advanced topics of models for continuous outcome with mass points, count models, and models for heterogeneous effects. Finally, they discuss endogeneity and how to address inference questions using data from complex surveys.The authors use their formidable experience to guide readers toward useful methods and away from less recommended ones. Their discussion of "health econometric myths" and the chapter presenting a framework for approaching health econometric estimation problems are especially useful for this aspect.Table of ContentsIntroduction Framework MEPS data The linear regression model: Specification and checks Generalized linear models Log and Box–Cox models Models for continuous outcomes with mass at zero Count models Models for heterogeneous effects Endogeneity Design effects

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Book SynopsisThe Mata Book: A Book for Serious Programmers and Those Who Want to Be is the book that Stata programmers have been waiting for. Mata is a serious programming language for developing small- and large-scale projects and for adding features to Stata. What makes Mata serious is that it provides structures, classes, and pointers along with matrix capabilities. The book is serious in that it covers those advanced features, and teaches them. The reader is assumed to have programming experience, but only some programming experience. That experience could be with Stata's ado language, or with Python, Java, C++, Fortran, or other languages like them. As the book says, "being serious is a matter of attitude, not current skill level or knowledge".The author of the book is William Gould, who is also the designer and original programmer of Mata, of Stata, and who also happens to be the president of StataCorp. Table of ContentsThe mechanics of using Mata. A programmer’s tour of Mata. Mata’s programming statements. Mata’s expressions. Mata’s variable types. Mata’s strict option and Mata’s pragmas. Mata’s function arguments. Programming example: n_choose_k() three ways. Mata’s structures. Programming example: Linear regression. Mata’s classes. Programming example: Linear regression 2. Better variable types. Programming constants. Mata’s associative arrays. Programming example: Sparse matrices. Programming example: Sparse matrices, continued. The Mata Reference Manual. Writing Mata code to add new commands to Stata. Mata’s storage type for complex numbers. How Mata differs from C and C++. Three-dimensional arrays (advanced use of pointers).

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Book SynopsisStata Tips provides concise and insightful notes about commands, features, and tricks that will help you obtain a deeper understanding of Stata.The book comprises the contributions of the Stata community that have appeared in the Stata Journal since 2003. Each tip is a brief article that provides practical advice on using Stata. With tips covering a breadth of topics in statistics, graphics, data management, and programming, both new and experienced Stata users are sure to find tips that will be useful in their research.Table of ContentsIntroducing Stata tips Stata tip 120: Certifying subroutines, M. L. Buis Stata tip 121: Box plots side by side, N. J. Cox Stata tip 122: Variable bar widths in two-way graphs, B. Jann Stata tip 123: Spell boundaries, N. J. Cox Stata tip 124: Passing temporary variables to subprograms, M. L. Buis Stata tip 125: Binned residual plots for assessing the fit of regression models for binary outcomes, J. Kasza Stata tip 126: Handling irregularly spaced high-frequency transactions data, C. F. Baum and S. Bibo Stata tip 127: Use capture noisily groups, R. B. Newson Stata tip 128: Marginal effects in log-transformed models: A trade application, L. J. Uberti Stata tip 129: Efficiently processing textual data with Stata’s new Unicode features, A. Koplenig Stata tip 130: 106610 and all that: Date variables that need to be fixed., N. J. Cox Stata tip 131: Custom legends for graphs that use translucency, T. P. Morris Stata tip 132: Tiny tricks and tips on ticks, N. J. Cox and V. Wiggins Stata tip 133: Box plots that show median and quartiles only, N. J. Cox Stata tip 134: Multiplicative and marginal interaction effects in nonlinear models, W. H. Dow, E. C. Norton, and J. T. Donahoe Stata tip 135: Leaps and bounds, M. L. Buis Stata tip 136: Between-group comparisons in a scatterplot with weighted markers, A. Musau Stata tip 137: Interpreting constraints on slopes of rank-deficient design matrices, D. Christodoulou Stata tip 138: Local macros have local scope, N. J. Cox Stata tip 139: The by() option of graph can work better than graph combine, N. J. Cox Stata tip 140: Shorter or fewer category labels with graph bar, N. J. Cox Stata tip 141: Adding marginal spike histograms to quantile and cumulative distribution plots, N. J. Cox Stata tip 142: joinby is the real merge m:m, D. Mazrekaj and J. Wursten Stata tip 143: Creating donut charts in Stata, A. Musau Stata tip 144: Adding variable text to graphs that use a by() option, N. J. Cox Stata tip 145: Numbering weeks within months, N. J. Cox Stata tip 146: Using margins after a Poisson regression model to estimate the number of events prevented by an intervention, M. Falcaro, R. B. Newson, and P. Sasieni Erratum: Stata tip 145: Numbering weeks within months, N. J. Cox Stata tip 147: Porting downloaded packages between machines, R. B. Newson Stata tip 148: Searching for words within strings, N. J. Cox Stata tip 149: Weighted estimation of fixed-effects and first-differences models, J. Gardner Stata tip 150: When is it appropriate to xtset a panel dataset with panelvar only? C. Lazzaro Stata tip 151: Puzzling out some logical operators, N. J. Cox Stata tip 152: if and if: When to use the if qualifier and when to use the if command, N. J. Cox and C. B. Schechter

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Book SynopsisFranz Buscha's book, Graphs Everyone Should Know and How to Create Them in Stata, is written for anyone who uses Stata to make graphs. Beginners will find a complete collection of tools for effectively visualizing their data and results. Experienced Stata users are certain to learn some new tricks as well.The chapters of the book are organized into four main sections: graphs for univariate data, graphs for bivariate data, graphs for multivariate data, and special graphs. Each chapter introduces a type of graph, explains when and why it is useful for visualizing a particular kind of data, demonstrates how to create that graph using Stata, and shows a few variations. The special graph section covers topics such as how to create maps, plot equations, create animated graphs, and create other specialty graphs.Readers will find it easy to learn to make graphs by example. Buscha demonstrates most graphs using datasets that are installed with your copy of Stata, so it is straightforward to follow along. He also clearly pairs each graph with the command used to create it in a box just above the graph. If you find a graph that you wish to create with your own data, you can take the command from the box and replace the variable names in the example with your own variable names.Buscha's book has two unique features that distinguish it from other books about Stata graphs. First, the book's goal is to clearly demonstrate how to effectively visualize different kinds of data and results from models using only necessary features. It focuses on important options but does not discuss all the options available for customizing each graph. Second, the book introduces many community-contributed graph commands that are freely available and can be downloaded from the internet. Readers may be unaware of these commands before finding them in this book, and they can learn how to use them quickly rather than spend time trying to write custom code for themselves.Graphs Everyone Should Know and How to Create Them in Stata is a reference you will use again and again as you visualize different types of data. You will quickly find the graphs that are applicable to your data and the Stata commands necessary to create them.

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Book SynopsisWhy can't we tickle ourselves? Which properties give you the best chance of winning Monopoly? What would happen if you fell into a black hole? Is it possible to hurt your brain if you think too much? In this entertaining and enlightening tour of day-to-day life, award-winning writer and scientist Robert Matthews tackles everything from the puzzling maths of odd socks to the real 'string theory' mystery: how does string acquire all those unwanted knots?Trade Review"simply fabulous." Jon

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Book SynopsisThis book provides a concise introduction to the mathematical foundations of time series analysis, with an emphasis on mathematical clarity. The text is reduced to the essential logical core, mostly using the symbolic language of mathematics, thus enabling readers to very quickly grasp the essential reasoning behind time series analysis. It appeals to anybody wanting to understand time series in a precise, mathematical manner. It is suitable for graduate courses in time series analysis but is equally useful as a reference work for students and researchers alike.Trade Review“‘This book provides a concise introduction to the mathematical foundations of time series analysis, with an emphasis on mathematical clarity. … It appeals to anybody wanting to understand time series in a precise, mathematical manner. It is suitable for graduate courses in time series analysis but is equally useful as a reference work for students and researchers alike.’ … The book can be recommended to all readers, who are interested in this field.” (Ludwig Paditz, zbMath 1414.62001, 2019)“This book is a rigorous, mathematically clear and self-contained and quite complete text on time series analysis, suitable both for graduate courses and as a reference book for researchers and users of stochastic temporal models.” (Nazaré Mendes Lopes, Mathematical Reviews, December, 2018)“Beran (Univ. of Konstanz, Germany) presents the mathematical foundations of time series analysis at a level suitable for advanced graduate students and researchers in statistics. The presentation is extremely concise … . the book gives definitions, theorems, and proofs, along with a few exercises and solutions. … it may be useful to graduate students and researchers as a reference.” (B. Borchers, Choice, Vol. 56 (03), November, 2018)​Table of Contents1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 What is a time series? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Time series versus iid data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Typical assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 Fundamental properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.1 Ergodic property with a constant limit . . . . . . . . . . . . . . . . . . . 52.1.2 Strict Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.3 Weak Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.4 Weak stationarity and Hilbert spaces . . . . . . . . . . . . . . . . . . . . 92.1.5 Ergodic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.1.6 Sufficient conditions for the a.s. ergodic property with a constant limit. . . . . . . . . . . 262.1.7 Sufficient conditions for the L2-ergodic property with a constant limit . .. . . . .. . . 272.2 Specific assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.2.1 Gaussian processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.2.2 Linear processes in L2(Ω) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.2.3 Linear processes with E(X2t ) = ∞ . . . . . . . . . . . . . . . . . . . . . . 342.2.4 Multivariate linear processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.2.5 Invertibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.2.6 Restrictions on the dependence structure . . . . . . . . . . . . . . . . . 493 Defining probability measures for time series . . . . . . . . . . . . . . . . . . . . . . 553.1 Finite dimensional distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.2 Transformations and equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.3 Conditions on the expected value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.4 Conditions on the autocovariance function . . . . . . . . . . . . . . . . . . . . . . 583.4.1 Positive semidefinite functions . . . . . . . . . . . . . . . . . . . . . . . . . 593.4.2 Spectral distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.4.3 Calculation and properties of F and f . . . . . . . . . . . . . . . . .4 Spectral representation of univariate time series . . . . . . . . . . . . . . . . . . . 814.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.2 Harmonic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.3 Extension to general processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.3.1 Stochastic integrals with respect to Z . . . . . . . . . . . . . . . . . . . . 844.3.2 Existence and definition of Z . . . . . . . . . . . . . . . . . . . . . . . . . . 894.3.3 Interpretation of the spectral representation . . . . . . . . . . . . . . 974.4 Further properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 984.4.1 Relationship between ReZ and ImZ . . . . . . . . . . . . . . . . . . . . 984.4.2 Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.4.3 Overtones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.4.4 Why are frequencies restricted to the range [-π,π]? . . . . . . . 1004.5 Linear filters and the spectral representation . . . . . . . . . . . . . . . . . . . . 1034.5.1 Effect on the spectral representation . . . . . . . . . . . . . . . . . . . . . 1034.5.2 Elimination of Frequency Bands . . . . . . . . . . . . . . . . . . . . . . . 1075 Spectral representation of real valued vector time series . . . . . . . . . . . . 1095.1 Cross-spectrum and spectral representation . . . . . . . . . . . . . . . . . . . . . 1095.2 Coherence and phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1166 Univariate ARMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.2 Stationary solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.3 Causal stationary solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1316.4 Causal invertible stationary solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 1336.5 Autocovariances of ARMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . 1346.5.1 Calculation by integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1346.5.2 Calculation using the autocovariance generating function . . . 1356.5.3 Calculation using the Wold representation . . . . . . . . . . . . . . . 1386.5.4 Recursive calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1396.5.5 Asymptotic decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1406.6 Integrated, seasonal and fractional ARMA and ARIMA processes . . 1476.6.1 Integrated processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1476.6.2 Seasonal ARMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1476.6.3 Fractional ARIMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . 1486.7 Unit roots, spurious correlation, cointegration . . . . . . . . . . . . . . . . . . . 1597 Generalized autoregressive processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1637.1 Definition of generalized autoregressive processes . . . . . . . . . . . . . . . 1637.2 Stationary solution of generalized autoregressive equations . . . . . . . . 1647.3 Definition of VARMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1687.4 Stationary solution of VARMA equations . . . . . . . . . . . . . . . . . . . . . . 1697.5 Definition of GARCH processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1717.6 Stationary solution of GARCH equations . . . . . . . . . . . . . . . . . . . . . . . 1727.7 Definition of ARCH(∞) processes . . . . . . . . . . . . . . . . . . . . .7.8 Stationary solution of ARCH(∞) equations . . . . . . . . . . . . . . . . . . . . . 1778 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1818.1 Best linear prediction given an infinite past . . . . . . . . . . . . . . . . . . . . . 1818.2 Predictability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1828.3 Construction of the Wold decomposition from f . . . . . . . . . . . . . . . . . 1878.4 Best linear prediction given a finite past . . . . . . . . . . . . . . . . . . . . . . . . 1909 Inference for µ, γ and F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1959.1 Location estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1959.2 Linear regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1979.3 Nonparametric estimation of γ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2059.4 Nonparametric estimation of f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21110 Parametric estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22710.1 Gaussian and quasi maximum likelihood estimation . . . . . . . . . . . . . . 22710.2 Whittle approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22910.3 Autoregressive approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23210.4 Model choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

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Book SynopsisFeedback control systems is an important course in aerospace engineering, chemical engineering, electrical engineering, mechanical engineering, and mechatronics engineering, to name just a few. Feedback control systems improve the system's behavior so the desired response can be acheived. The first course on control engineering deals with Continuous Time (CT) Linear Time Invariant (LTI) systems. Plenty of good textbooks on the subject are available on the market, so there is no need to add one more. This book does not focus on the control engineering theories as it is assumed that the reader is familiar with them, i.e., took/takes a course on control engineering, and now wants to learn the applications of MATLAB® in control engineering. The focus of this book is control engineering applications of MATLAB® for a first course on control engineering.Table of ContentsPreface.- Acknowledgments.- Introduction to MATLAB®.- Commonly Used Commands in Analysis of Control Systems.- Introduction to Simulink®.- Controller Design in MATLAB®.- Introduction to System Identification Toolbox™.- References.- Authors' Biographies.

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Book SynopsisA lot of digital ink has been spilled on "big data" over the past few years. Most of this surge owes its origin to the various types of unstructured data in the wild, among which the proliferation of text-heavy data is particularly overwhelming, attributed to the daily use of web documents, business reviews, news, social posts, etc., by so many people worldwide.A core challenge presents itself: How can one efficiently and effectively turn massive, unstructured text into structured representation so as to further lay the foundation for many other downstream text mining applications? In this book, we investigated one promising paradigm for representing unstructured text, that is, through automatically identifying high-quality phrases from innumerable documents. In contrast to a list of frequent n-grams without proper filtering, users are often more interested in results based on variable-length phrases with certain semantics such as scientific concepts, organizations, slogans, and so on. We propose new principles and powerful methodologies to achieve this goal, from the scenario where a user can provide meaningful guidance to a fully automated setting through distant learning. This book also introduces applications enabled by the mined phrases and points out some promising research directions.Table of ContentsAcknowledgments.- Introduction.- Quality Phrase Mining with User Guidance.- Automated Quality Phrase Mining.- Phrase Mining Applications.- Bibliography.- Authors' Biographies .

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Book Synopsis- Part I: Stochastics and Statistical Theory.- Strong Gaussian Approximations with Random Multipliers.- Selection of Parametric Copula Models in the Approximation of Copulas using Cramér-von Mises Divergence.- Multivariate Dependence Based on Diagonal Sections: Spearman’s Footrule and Related Measures.- Proportional Asymptotics of Piecewise Exponential Proportional Hazards Models.- On the Choice of the Two Tuning Parameters for Nonparametric Estimation of an Elliptical Distribution Generator.- Part II: Inference and Machine Learning.- Inference from Longitudinal Data by Clustering and Machine Learning.- The Use of Neural Networks and PCA Dimensionality Reduction in the Imputation of Missing Fragments in High-Dimensional Time Series.- Discrete-Valued Time Series and Recurrent Neural Network Response Functions.- Application of Model-Free Time-Series Segmentation to Study Sleep in Mice.- Part III: Detection of Patterns in Data.- Testing for Dependence by Using Ordinal Patterns: Survey and Perspectives.- On Some Properties and Testing of Benford’s Law.

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Book SynopsisThe monograph is devoted to one of the most important trends in contemporary mathematical physics, the investigation of evolution equations of many-particle systems of statistical mechanics. The book systematizes rigorous results obtained in this field in recent years, and it presents contemporary methods for the investigation of evolution equations of infinite-particle systems. The book is intended for experts in statistical physics, mathematical physics, and probability theory and for students of universities specialized in mathematics and physics.Trade Review"This book may be useful for advanced graduate students and for scientists who are interested in mathematical problems of the statistical mechanics and rare ed gasesow.?"Oleg A. Sinkevich in: Zentralblatt Math 1/2010<

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Book SynopsisThis textbook teaches crucial statistical methods to answer research questions using a unique range of statistical software programs, including MINITAB and R. This textbook is developed for undergraduate students in agriculture, nursing, biology and biomedical research. Graduate students will also find it to be a useful way to refresh their statistics skills and to reference software options. The unique combination of examples is approached using MINITAB and R for their individual strengths. Subjects covered include among others data description, probability distributions, experimental design, regression analysis, randomized design and biological assay. Unlike other biostatistics textbooks, this text also includes outliers, influential observations in regression and an introduction to survival analysis. Material is taken from the author's extensive teaching and research in Africa, USA and the UK. Sample problems, references and electronic supplementary material accompany each chapter.Table of Contents​Table of Contents attached as well. Introduction.- Frequency Distributions.- Numerical Description of Data.- Probability and Probability Distributions.- Estimation and Hypothesis Testing.- Regression Analysis.- Categorical Data Analysis.- Experimental Design.- The Completely Randomized Design.- The Randomized Complete Block Design.- Multiple Blocking Designs.- Analysis of Covariance.- Factorial Treatments Designs.- The Split-Plot Design.- Incomplete Block Design.- Quantal-Bioassay.- Repeated Measures Design.- Survival Analysis.

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Book SynopsisThis volume presents five different methods recently developed to tackle the large scale behavior of highly correlated random systems, such as spin glasses, random polymers, local times and loop soups and random matrices. These methods, presented in a series of lectures delivered within the Jean-Morlet initiative (Spring 2013), play a fundamental role in the current development of probability theory and statistical mechanics. The lectures were: Random Polymers by E. Bolthausen, Spontaneous Replica Symmetry Breaking and Interpolation Methods by F. Guerra, Derrida's Random Energy Models by N. Kistler, Isomorphism Theorems by J. Rosen and Spectral Properties of Wigner Matrices by B. Schlein.This book is the first in a co-edition between the Jean-Morlet Chair at CIRM and the Springer Lecture Notes in Mathematics which aims to collect together courses and lectures on cutting-edge subjects given during the term of the Jean-Morlet Chair, as well as new material produced in its wake. It is targeted at researchers, in particular PhD students and postdocs, working in probability theory and statistical physics.Table of Contents1 Random Polymers.- 2 Spontaneous replica symmetry breaking and interpolation methods for complex statistical mechanics systems.- 3 Derrida’s random energy models: from spin glasses to the extremes of correlated random fields.- 4 Isomorphism Theorems: Markov processes, Gaussian processes and beyond.- 5 Spectral properties of Wigner matrices.

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Book SynopsisEndlich verstehen Sie die ökonomischen Anwendungsmöglichkeiten und Funktionsweisen statistischer Wahrscheinlichkeiten im Betrieb! Dieses Buch vermittelt Ihnen die grundlegenden Verfahren der Wahrscheinlichkeitsrechnung als auch der Wahrscheinlichkeitsverteilungen und zeigt Ihnen deren praktische Anwendung in Betrieb und Ökonomie. Beispiele und Fragen mit Musterlösungen dienen dem weiteren Verständnis.Table of ContentsGrundlagen statistischer Wahrscheinlichkeiten in der Betriebswirtschaft: Grundbegriffe der Wahrscheinlichkeitsrechnung Diskrete Wahrscheinlichkeitsverteilungen - Binomial- und Hypergeometrische Verteilung Stetige Wahrscheinlichkeitsverteilung - Normalverteilung Intervallschätzung Notwendiger Stichprobenumfang Wahlforschung Hypothesentestverfahren Tabelle der Standardnormalverteilung Mathematische Grundlagen der induktiven Statistik Lösungen

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Book SynopsisIn den empirischen Sozialwissenschaften dienen die Methoden und Techniken der Statistik der Auswertung von Ergebnissen empirischer Untersuchungen und ermöglicht so die Beschreibung der quantitiativen Eigenschaften einer beobachteten und vollständig erfassten Gruppe. Das vorliegende Buch beschäftigt sich nahezu ausschließlich mit deskriptiver Statistik, welche sich mit der Aufbereitung und Beschreibung von Datenmengen und deren Verteilung befasst. Nach einer ausführlichen und grundlegenden Einführung in das Thema werden die wichtigsten Häufigkeitsverteilungen sowie die Maßzahlen zu deren Beschreibung dargestellt. Mit der linearen Einfachregression wird zuletzt der lineare funktionale Zusammenhang zweier Variabler erläutert. Zu jedem Kapitel gibt es Beispiele, Übungsaufgaben und eine Zusammenfassung. Im Anhang befinden sich mehrere Klausuren mit Lösungen, die in den letzten Jahren an der TU Dresden benutzt wurden.Table of Contents1 Grundlagen.- 1.1 Geisteswissenschaften und empirische Wissenschaften heute.- 1.2 Grundmethoden der empirischen Wissenschaften.- 1.2.1 Untersuchungsformen.- 1.2.2 Datenerhebungstechniken.- 1.2.3 Auswahlverfahren.- 1.3 Ablauf empirischer Sozialforschung: Der Forschungsprozess.- 1.3.1 Auswahl des Forschungsgegenstandes.- 1.3.2 Theoriebildung.- 1.3.3 Planung der Untersuchung.- 1.3.4 Durchführung der Untersuchung (Datenerhebung).- 1.3.5 Beschreibung und Zusammenfassung der Ergebnisse.- 1.3.6 Verallgemeinerung der Ergebnisse und Publikation.- 1.4 Einführung in die Forschungsstatistik.- 1.4.1 Statistische Gesetzmäßigkeiten.- 1.4.2 Grundlegende statistische Begriffe.- 1.4.3 Statistische Symbole.- 1.5 Begriff des Messens und der Messskalen.- 1.5.1 Der Begriff des Messens.- 1.5.2 Die Messniveaus.- 1.5.3 Die Bedeutung der Messniveaus für die Statistik.- 1.5.4 Gütekriterien der Messung.- Aufgaben.- 2 Empirische Häufigkeitsverteilungen.- 2.1 Häufigkeit und Verteilung.- 2.1.1 Das Aufstellen einer Häufigkeitstabelle.- 2.1.2 Absolute, relative und prozentuale Häufigkeiten.- 2.1.3 Die Häufigkeitsfunktion.- 2.1.4 Die Empirische Verteilungsfunktion.- 2.2 In Klassen eingeteilte Merkmale.- 2.2.1 Das Einteilen der Messwerte in Klassen.- 2.2.2 Aufstellen der Klassenhäufigkeiten.- 2.2.3 Offene Klassen.- 2.2.4 Exakte Klassengrenzen.- 2.2.5 Repräsentation einer Klasse durch die K1assenmitte.- 2.2.6 Informationsverlust durch Klasseneinteilung.- 2.3 Graphische Darstellungen von Häufigkeitsverteilungen.- 2.3.1 Das Stab-oder Balkendiagramm.- 2.3.2 Das Kreisdiagramm.- 2.3.3 Das Histogramm.- 2.3.4 Das Polygon.- 2.3.5 Typische Fonnen spezieller Verteilungen.- 2.4 Erkennen von Fehlinformation in statistischen Analysen.- 3 Maßzahlen eindimensionaler Verteilungen.- 3.1 Lageparameter.- 3.1.1 Das arithmetische Mittel.- 3.1.2 Der Median.- 3.1.3 Der Modus.- 3.1.4 Relative Positionen.- 3.1.5 Zulässige und optimale Lageparameter der einzelnen Messniveaus.- 3.2 Dispersionsparameter.- 3.2.1 Spannweite.- 3.2.2 Der (mittlere) Quartilabstand.- 3.2.3 Standardabweichung und Varianz.- 3.2.4 Der Variationskoeffizient zum Vergleich mehrerer Stichproben.- 3.2.5 Die Zusammenfassung von Varianzen.- 3.2.6 Gesamtvarianz, systematische Varianz und Fehlervarianz.- 3.2.7 Die Summe der quadratischen Abweichungen.- Aufgaben.- 4 Maßzahlen zweidimensionaler Verteilungen.- 4.1 Vorbemerkungen.- 4.1.1 Linearität.- 4.1.2 Die gemeinsame Verteilung.- 4.1.3 Ein einfaches Beispiel zur Darstellung bivariater Verteilungen.- 4.2 Korrelation.- 4.2.1 Intervallniveau.- 4.2.2 Ordinalniveau.- 4.3 Nomina1niveau.- 4.3.1 Tau (Goodman und Kruskal).- 4.3.2 Lambda.- 4.3.3 Kontingenzkoeffizient.- 4.3.4 Phi.- 4.3.5 Cramer’s V.- 4.4 Interpretation.- 5 Die lineare Einfachregression.- 5.1 Anpassen von Kurven.- 5.2 Vorhersage bei korrelierten Variablen.- 5.3 Methode der kleinsten Quadrate.- 5.3.1 Berechnung der Regressionsgeraden Gy/x.- 5.3.2 Berechnung der Regressionsgeraden Gx/y.- 5.4 Regressionskoeffizient, Korrelationskoeffizient und Varianz.- 5.5 Der Korrelationskoeffizient als Maß für die Güte der Regression.- 5.5.1 Die Varianz um die Regressionsgerade Sy/x2.- 5.5.2 Die Varianz auf der Regressionsgeraden $$ s_{\tilde y}^2 $$.- 5.6 Berechnung zweier Beispielaufgaben.- 5.6.1 Beispiel 1.- 5.6.2 Beispiel 2.- Weiterführende Literatur.- Anhang 1 Probeklausuren.- Anhang 2 Lösungen zu den Probeklausuren.

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Book SynopsisIsoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.Trade ReviewThis book gives an excellent, almost complete account of the whole subject of probability in Banach spaces, a branch of probability theory that has undergone vigorous development... There is no doubt in the reviewer's mind that this book [has] become a classic. MathSciNetAs the authors state, "this book tries to present some of the main aspects of the theory of probability in Banach spaces, from the foundation of the topic to the latest developments and current research questions''. The authors have succeeded admirably… This very comprehensive book develops a wide variety of the methods existing … in probability in Banach spaces. … It [has] become an event for mathematicians… Zentralblatt MATHTable of ContentsNotation.- 0. Isoperimetric Background and Generalities.- 1. Isoperimetric Inequalities and the Concentration of Measure Phenomenon.- 2. Generalities on Banach Space Valued Random Variables and Random Processes.- I. Banach Space Valued Random Variables and Their Strong Limiting Properties.- 3. Gaussian Random Variables.- 4. Rademacher Averages.- 5. Stable Random Variables.- 6 Sums of Independent Random Variables.- 7. The Strong Law of Large Numbers.- 8. The Law of the Iterated Logarithm.- II. Tightness of Vector Valued Random Variables and Regularity of Random Processes.- 9. Type and Cotype of Banach Spaces.- 10. The Central Limit Theorem.- 11. Regularity of Random Processes.- 12. Regularity of Gaussian and Stable Processes.- 13. Stationary Processes and Random Fourier Series.- 14. Empirical Process Methods in Probability in Banach Spaces.- 15. Applications to Banach Space Theory.- References.

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Book SynopsisThis monograph is the r st in Fuzzy Approximation Theory. It contains mostly the author s research work on fuzziness of the last ten years and relies a lot on [10]-[32] and it is a natural outgrowth of them. It belongs to the broader area of Fuzzy Mathematics. Chapters are self-contained and several advanced courses can be taught out of this book. We provide lots of applications but always within the framework of Fuzzy Mathematics. In each chapter is given background and motivations. A c- plete list of references is provided at the end. The topics covered are very diverse. In Chapter 1 we give an extensive basic background on Fuzziness and Fuzzy Real Analysis, as well a complete description of the book. In the following Chapters 2,3 we cover in deep Fuzzy Di?erentiation and Integ- tion Theory, e.g. we present Fuzzy Taylor Formulae. It follows Chapter 4 on Fuzzy Ostrowski Inequalities. Then in Chapters 5, 6 we present results on classical algebraic and trigonometric polynomial Fuzzy Approximation.Table of ContentsABOUT H-FUZZY DIFFERENTIATION.- ON FUZZY TAYLOR FORMULAE.- FUZZY OSTROWSKI INEQUALITIES.- A FUZZY TRIGONOMETRIC APPROXIMATION THEOREM OF WEIERSTRASS-TYPE.- ON BEST APPROXIMATION AND JACKSON-TYPE ESTIMATES BY GENERALIZED FUZZY POLYNOMIALS.- BASIC FUZZY KOROVKIN THEORY.- FUZZY TRIGONOMETRIC KOROVKIN THEORY.- FUZZY GLOBAL SMOOTHNESS PRESERVATION.- FUZZY KOROVKIN THEORY AND INEQUALITIES.- HIGHER ORDER FUZZY KOROVKIN THEORY USING INEQUALITIES.- FUZZY WAVELET LIKE OPERATORS.- ESTIMATES TO DISTANCES BETWEEN FUZZY WAVELET LIKE OPERATORS.- FUZZY APPROXIMATION BY FUZZY CONVOLUTION OPERATORS.- DEGREE OF APPROXIMATION OF FUZZY NEURAL NETWORK OPERATORS, UNIVARIATE CASE.- HIGHER DEGREE OF FUZZY APPROXIMATION BY FUZZY WAVELET TYPE AND NEURAL NETWORK OPERATORS.- FUZZY RANDOM KOROVKIN THEOREMS AND INEQUALITIES.- FUZZY-RANDOM NEURAL NETWORK APPROXIMATION OPERATORS, UNIVARIATE CASE.- -SUMMABILITY AND FUZZY KOROVKIN APPROXIMATION.- -SUMMABILITY AND FUZZY TRIGONOMETRIC KOROVKIN APPROXIMATION.- UNIFORM REAL AND FUZZY ESTIMATES FOR DISTANCES BETWEEN WAVELET TYPE OPERATORS AT REAL AND FUZZY ENVIRONMENT.

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Book SynopsisIn Part I of this report the pointwise derivation of scalar set functions is investigated, first along the lines of R. DE POSSEL (abstract derivation basis) and A. P. MORSE (blankets); later certain concrete situations (e. g. , the interval basis) are studied. The principal tool is a Vitali property, whose precise form depends on the derivation property studied. The "halo" (defined at the beginning of Part I, Ch. IV) properties can serve to establish a Vitali property, or sometimes produce directly a derivation property. The main results established are the theorem of JESSEN-MARCINKIEWICZ-ZYGMUND (Part I, Ch. V) and the theorem of A. P. MORSE on the universal derivability of star blankets (Ch. VI) . . In Part II, points are at first discarded; the setting is somatic. It opens by treating an increasing stochastic basis with directed index sets (Th. I. 3) on which premartingales, semimartingales and martingales are defined. Convergence theorems, due largely to K. KRICKEBERG, are obtained using various types of convergence: stochastic, in the mean, in Lp-spaces, in ORLICZ spaces, and according to the order relation. We may mention in particular Th. II. 4. 7 on the stochastic convergence of a submartingale of bounded variation. To each theorem for martingales and semi-martingales there corresponds a theorem in the atomic case in the theory of cell (abstract interval) functions. The derivates concerned are global. Finally, in Ch.Table of ContentsI Pointwise Derivation.- I: Derivation Bases.- 1. Setting and general notation.- 2. dePossel’s derivation basis.- 3. Examples of bases.- 4. Pretopological notions.- 5. Comparison lemmas.- II: Derivation Theorems for ?-additive Set Functions under Assumptions of the Vitali Type.- 1. The individual Vitali assumption.- 2. The individual full derivation theorem for Radon or ?-fmite ?-integrals.- 3. The individual full derivation theorem for Radon measures.- 4. Class derivation theorems.- 5. Relation to Younovitch’s derivation theorem.- 6. The strong Vitali property.- 7. Half-regular and regular branches of a derivation basis.- III: The Converse Problem I: Covering Properties Deduced from Derivation Properties of ?-additive Set Functions.- 1. dePossel’s equivalence theorem.- 2. A necessary and sufficient condition for a weak derivation basis to derive a ?-finite ?-measure (Radon measure) ?.- 3. Younovitch’s equivalence theorem.- 4. A converse theorem for bases deriving the ?(q)-functions, q ? 1.- IV: Halo Assumptions in Derivation Theory. Converse Problem II.- 1. A. P. Morse’s halo properties.- 2. Abstract version of the strong Vitali theorem modelled after Banach.- 3. Abstract version of the strong Vitali theorem modelled after Carathéodory.- 4. Weak halo evanescence condition.- 5. Further criteria for the validity of the Density Theorem involving the weak halo.- 6. An individual derivability condition of Busemann-Feller type.- 7. The weak halo property in general bases.- 8. Product invariance of a weak halo property.- V: The Interval Basis. The Theorem of Jessen-Marcin-Kiewicz-Zygmund.- 1. The interval basis as a weak derivation basis.- 2. Theorem of Jessen-Marcinkiewicz-Zygmund.- 3. Properties of the halo function as consequences of derivation properties.- 4. Saks’ counterexample.- 5. The parallelepipedon basis.- 6. Saks’ “rarity” theorem.- VI: A. P. Morse’s Blankets.- 1. Nets.- 2. Hives.- 3. Fundamental covering theorems.- 4. Star blankets.- II Martingales and Cell Functions.- I: Theory without an Intervening Measure.- 1. Additive functions.- 2. ?-additive functions.- 3. Premartingales, semi-martingales, and martingales.- 4. Ordered space of martingales of basis(??).- 5. Integrals of premartingales.- 6. Martingales and additive functions.- 7. ?-additive martingales.- 8. Induced martingales.- 9. Premartingales and cell functions.- 10. Integrals of cell functions.- 11. Convergence theorems for martingales of bounded variation when ? is a measure algebra.- II: Theory in a Measure Space without Vitali Conditions.- 1. Preliminaries.- 2. Absolutely continuous and singular premartingales.- 3. Stochastic processes.- 4. Stochastic convergence.- 5. Mean convergence of order 1.- 6. Convergence in Orlicz spaces.- 7. Cell functions.- III: Theory in a Measure Space with Vitali Conditions.- 1. Preliminaries and definitions.- 2. Vitali conditions.- 3. Order convergence of martingales.- 4. Necessity of the Vitali conditions.- 5. Order convergence of submartingales.- 6. Order convergence of cell functions.- IV: Applications.- 1. Pointwise setting.- 2. Specifically pointwise concepts and results. Convergence almost everywhere.- 3. Martingales in the classical sense.- 4. Product spaces.- 5. The Radon- Nikodym integrand defined as a derivate.- 6. Representation of the spaces Lx as spaces of cell functions.- 7. Pointwise derivation of cell functions.- 8. Examples of concrete cell bases.- 9. Stochastic bases on a group.- Complements.- 1°. Derivation of vector-valued integrals.- 2°. Functional derivatives.- 3°. Topologies generated by measures.- 4°. Vitali’s theorem for invariant measures.- 5°. Global derivatives in locally compact topological groups..- 6°. Submartingales with decreasing stochastic bases.- 7°. Vector-valued martingales and derivation.- 9°. Derivation of measures.

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Book SynopsisDie Statistik und ihre Anwendung in unserem Leben in 101 Stichwörtern kurz, prägnant und verständlich erklären kann nur Walter Krämer. Ob es um die Zusammensetzung der Arbeitslosenquote geht, Aktienkurse, Wahlprognosen, Intelligenzquotient, polizeiliche Kriminalstatistik oder um Klinische Studien und Big Data: Der Leser erhält genau die Informationen, die er benötigt, um im täglichen Leben mit Statistik sinnvoll umgehen zu können. Dazu muss man kein Rechen-As sein oder Mathematik studiert haben. Ein gesunder Menschenverstand und die Bereitschaft, den Tatsachen ohne Vorurteile ins Gesicht zu sehen reichen vollkommen aus, um die Kunst der Statistik schätzen zu lernen: den Schein vom Sein zu trennen und die Stecknadel im Heuhaufen zu finden. Dieses Buch ist ein gleichermaßen verständlicher, faszinierender, amüsanter wie auch und hilfreicher als Ratgeber für unseren täglichen Umgang mit Statistik: denn nur wer versteht kann mitreden und entlarven.Trade Review“... Das Lesen dieses statistischen Wörter- Büchleins wird jenen am meisten Freude bereiten und Nutzen bringen, die sich, selbst Nichtstatistiker, aus unterschiedlichen Gründen - sei es beruflich oder im Studium - mit dem Fach auseinandersetzen müssen. Für diese Leserschaft ist es absolut lesenswert, lehrreich und auch launig geschrieben - ein Krämer eben! ...” (Andreas Quatember, in: Austrian Journal of Statistics, Jg. 46, Heft 1, Februar 2017)“Praktisches alphabetisch sortiertes Nachschlagewerk ... Die Begriffe werden jeweils kurz, leicht verständlich und nachvollziehbar anhand kleiner Beispiele Erläutert …” (Sandra Fuchs, in: Psychologie FoxBlog, sanfuchs1979.wordpress.com, 25. Mai 2016)

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Book SynopsisVier von zehn oder jeder Vierte ...Ein Blick in eine beliebige Tageszeitung genügt: Statistiken sind ohne Zweifel ein wesentlicher Bestandteil unserer Informationsgesellschaft. Dennoch ist das Image des Faches Statistik denkbar schlecht. Die Diskrepanz zwischen offenkundiger Bedeutung und schlechtem Ruf beruht zum Teil auf dem fundamentalen Irrtum, die Qualität der statistischen Methoden mit der Qualität ihrer Anwendung zu verwechseln. Denn ob aus Unachtsamkeit, Unverständnis oder Unvermögen: In den Medien wird mit Statistiken allzu oft Des-Information statt Information betrieben. Dieses Buch lädt die Leser zu einer kritischen und amüsanten Irrfahrt durch falsche Schlagzeilen und unsinnige Interpretationen statistischer Ergebnisse in Tageszeitungen oder Zeitschriften ein. Staunen Sie darüber, dass ein Viertel aller Studierenden alkoholabhängig ist, dass Männer ihren Rasierern treuer sind als ihren Partnerinnen, dass höherer Schokoladenkonsum mehr Nobelpreisträger erzeugt – und warum das alles blanker Unsinn ist.Aber Achtung: Dieses Buch kann Sie zu einem mündigeren Zeitungsleser machen!Trade Review“... hochaktuell und vor allem sehr lesenswert. ... liefert Quatember mit seinem Buch das nötige Basiswissen ...” (Barbara Denscher, in: Flaneurin, flaneurin.at, Mai 2020)“… Ein amüsant zu lesendes Büchlein ... so facettenreich, dass es als Lehrbuch verbreiteter Fehler gelten kann.” (in: Wasser und Abfall, Jg. 17, Heft 12, Dezember 2015)“... Das Werk gibt einen systematischen Überblick über typische Fehler, bespricht sie ausführlich und erklärt die mathematischen Zusammenhänge dahinter ...” (Roland Pilous, in: Spektrum.de, 9. September 2015)Table of ContentsEs ist nicht alles Gold, was glänzt.- 101 % zufriedene Kunden.- Ein Bild sagt mehr als tausend Worte.- Unvergleichliche Mittelwerte.- Mit Statistik lässt sich alles beweisen!.- Die Repräsentativitätslüge.- Der PISA-Wahnsinn.- Tatort Lotto.- Einen hab ich noch!.

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Book SynopsisDieses Buch beschäftigt sich mit den praktischen Fragestellungen statistischer Erhebungen (= Surveys) wie sie sich etwa in der empirischen akademischen Forschung, der offiziellen Statistik oder der kommerziellen Markt- und Meinungsforschung stellen: Wodurch unterscheiden sich verschiedene Stichprobendesigns? Wie sind sie praktisch umzusetzen (z. B. mit der Statistik-Freeware R)? Wie lassen sich die Daten- und die Ergebnisqualität beeinflussen? Wie kompensiert man Nonresponse? Wie können nichtzufällige Stichprobenverfahren und Big Data-Analysen im Zusammenhang mit den Aufgaben der Survey-Statistik funktionieren? Die Vermittlung des Methodenverständnisses wird unterstützt durch die verständnisorientierte Veranschaulichung der Basisideen. Diese Anschaulichkeit wird durch einfache und daher gut nachvollziehbare Beispiele gestützt. Für die vorliegende 3. Auflage wurde das Buch vollständig überarbeitet und inhaltlich unter anderem um die Betrachtung des Spannungsfeldes zwischen Survey-Theorie und -Praxis, die Grundlagen des Simulationsansatzes der Survey-Statistik und eine Auseinandersetzung mit den sich zunehmender Beliebtheit erfreuenden nichtzufälligen Stichprobenverfahren (inklusive den damit verwandten Big Data-Generierungsprozessen) erweitert. Jedes Kapitel wird zudem durch Aufgabenstellungen ergänzt, deren Umsetzung mit der Software R angeleitet wird.Table of ContentsVom Teil aufs Ganze – Einführung in die Stichprobentheorie.- Die Mutter aller Zufallsstichprobenverfahren – Die uneingeschränkte Zufallsauswahl.- Es geht auch anders – Weitere Schätzmethoden.- Zerlegen macht’s genauer – Die geschichtete uneingeschränkte Zufallsauswahl.- Nahe Liegendes gemeinsam erheben spart Geld – Die uneingeschränkte Klumpenauswahl.- Nahe beisammen und doch auseinander – Die zweistufige uneingeschränkte Zufallsauswahl.- Grenzt an Zauberei – Die größenproportionale Zufallsauswahl.- Welcher Zweck heiligt solche Mittel? - Die nichtzufälligen Auswahlen.- Anhang.- Literatur.- Sachverzeichnis.

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Book Synopsis

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Book SynopsisIn die 4. Auflage dieser Aufgabensammlung wurde eine in Aufgaben-Form gebrachte empirische Untersuchung über das Lotto 6 aus 49 aufgenommen, die auf der Auswertung von 1264 Lotto-Ausspielungen aus 25 Jahren beruht. Das Ergebnis lautet: Auch aus Sicht der Mathematischen Statistik gibt es rationale Tipp-Strategien. Sie lassen sich darauf gründen, daß die realen Lottospieler-Kollektive einem stark ausgeprägten Konsensverhalten folgen, das rationales individuelles Verhalten in der Form eines speziellen Gegen-den-Strom-Schwimmens ermöglicht. Allein die systematische Berücksichtigung einer einzigen kollektiv stark vernachlässigten Lottozahl - solche Zahlen werden als "Antikonsenszahlen" bezeichnet - hätte in den untersuchten Ausspielungen die mathematische Gewinn-Erwartung um ca. 30% erhöht gegenüber dem "Normal"-Wert von 50% des Einsatzes. Danach erscheint es hoch plausibel, daß Spieler, die ihre Tippreihen ausschließlich aus solchen "Antikonsenszahlen" bilden, sogar eine mathematische Gewinn-Erwartung erzielen können, die den Einsatz übersteigt. Ein Bereich solcher "Antikonsenszahlen" wird mit Hilfe eines statistischen Schätzverfahrens explizit bestimmt. Die praktische Nutzanwendung solcher Ergebnisse steht allerdings unter dem Vorbehalt, daß sich das kollektive Spielverhalten nicht signifikant ändert, z.B. weil es durch Informationen - wie die hier vorgelegten - gestört wird.Table of ContentsAufgabensammlung zur statistischen Methodenlehre und Wahrscheinlichkeitsrechnung.

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Book SynopsisTable of Contents1 Einleitung.- I Motivation, Asymptotik und Modifikationen von Kern- und Nearest-Neighbour-Schätzern.- 2 Von der nichtparametrischen Dichteschätzung zur nichtparametrischen Zeitreihenanalyse und Prognose.- 2.1 Nichtparametrische Dichteschätzung.- 2.2 Nichtparametrische Regression.- 2.3 Nichtparametrische Zeitreihenanalyse und Prognose.- 3 Asymptotische Eigenschaften von Kern- und Nearest-Neighbour-Schätzern.- 3.1 Modellannahmen zur Herleitung asymptotischer Eigenschaften.- 3.2 Asymptotische Eigenschaften bei unabhängigen Beobachtungen.- 3.3 Asymptotische Eigenschaften bei abhängigen Beobachtungen.- 4 Ein Lösungsansatz zum Problem der Dimensionalität.- 4.1 Prognose auf der Basis ähnlicher aber möglicherweise entfernter Verlaufsmuster.- 4.2 Verringerung des Einflusses allzu ferner Verlaufsmuster.- 5 Biasreduktion durch asymmetrische Kerne.- 5.1 Der Fall p=1.- 5.2 Übertragung auf höhere Dimensionen.- 6 Biasreduzierende und varianzreduzierende Mischungen von Kern- und NN-Schätzern.- 7 Robuste Kern- und NN-Schätzer.- 7.1 M-Schätzer.- 7.2 L-Schätzer.- 7.3 R-Schätzer.- 7.4 Weitere Verfahren der robusten Kern- und Nearest-Neighbour-Schätzung.- 8 Weitere Modifikationen und einige Bemerkungen zur Wahl der Glättungsparameter.- 8.1 Additive nichtparametrische Modelle.- 8.2 Twicing.- 8.3 Jackknifing von Kern- und Nearest- Neighbour-Schätzern.- 8.4 Polynomiale nichtparametrische Regression.- 8.5 Semiparametrische Zeitreihenmodelle.- 8.6 Einige Bemerkungen zur Wahl der Bandweite und der Anzahl der nächsten Nachbarn.- II Einige empirische Studien.- 9 Nichtparametrische Modellierung der Wasserführung der Ruhr.- 9.1 Die Daten.- 9.2 Prediktogramme.- 9.3 Kern- und NN-Schätzer.- 9.4 Modifizierte Kern- und NN-Schätzer.- 10 Nichtparametrische Modellierung der Leitfähigkeit eines niedersächsischen Flusses.- 10.1 Die Daten.- 10.2 Prognoseeigenschaften gewöhnlicher NN-Schätzer.- 10.3 Verwendung asymmetrischer Kernfunktionen.- 10.4 Einbeziehen ähnlicher aber möglicherweise entfernter Verläufe.- 11 Nichtparametrische Modellierung der Luftbelastung durch Schwefeldioxid und Stickstoffdioxid.- 11.1 Allgemeines.- 11.2 Die Daten.- 11.3 Prognosen.- 12 Abschließende Bemerkungen.- Abbildungsverzeichnis.- Tabellenverzeichnis.

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Book SynopsisOne SCI\'ice mathematics bas rendered the 'Et moi, ...si j'avait su comment en revcnir. je n'y serais point aile: human race. It bas put common sc:nsc back where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Hcavisidc Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly. all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. :; 'One service logic has rendered com- puter science .. :; 'One service category theory has rendered mathematics .. :. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.Table of Contents0. Preliminary Informationh.- 0.1 Probability Space.- 0.2 Random Functions and Processes.- 0.3 Conditional Probabilities.- 0.4 Independence.- 1. Sums of Independent Random Variables.- 1.1 Main Inequalities.- 1.2 Renewal Scheme.- 1.3 Random Walks. Recurrence.- 1.4 Distribution of Ladder Functions.- 2. General Processes with Independent Increments (Random Measures).- 2.1 Nonnegative Random Measures with Independent Values (r.m.i.v.).- 2.2 Random Measures with Alternating Signs.- 2.3 Stochastic Integrals and Countably Additive r.m.i.v.- 2.4 Random Linear Functional and Generalized Functions.- 3. Processes with Independent Increments. General Properties.- 3.1 Decomposition of a Process. Properties of Sample Functions.- 3.2 Stochastically Continuous Processes.- 3.3 Properties of Sample Functions.- 3.4 Locally Homogeneous Processes with Independent Increments.- 4. Homogeneous Processes.- 4.1 General Properties.- 4.2 Additive Functionals.- 4.3 Composed Poisson Process.- 4.4 Homogeneous Processes in R.- 5. Multiplicative Processes.- 5.1 Definition and General Properties.- 5.2 Multiplicative Processes in Abelian Groups.- 5.3 Stochastic Semigroups of Linear Operators in Rd.- Notes.- References.

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