Understand and utilize the latest developments in Weibull inferential methods

While the Weibull distribution is widely used in science and engineering, most engineers do not have the necessary statistical training to implement the methodology effectively. "Using the Weibull Distribution: Reliability, Modeling, " "and Inference "fills a gap in the current literature on the topic, introducing a self-contained presentation of the probabilistic basis for the methodology while providing powerful techniques for extracting information from data.

The author explains the use of the Weibull distribution and its statistical and probabilistic basis, providing a wealth of material that is not available in the current literature. The book begins by outlining the fundamental probability and statistical concepts that serve as a foundation for subsequent topics of coverage, including:

- Optimum burn-in, age and block replacement, warranties

and renewal theory

- Exact inference in Weibull regression

- Goodness of fit testing and distinguishing the Weibull

from the lognormal

- Inference for the Three Parameter Weibull

Throughout the book, a wealth of real-world examples showcases the discussed topics and each chapter concludes with a set of exercises, allowing readers to test their understanding of the presented material. In addition, a related website features the author's own software for implementing the discussed analyses along with a set of modules written in Mathcad(R), and additional graphical interface software for performing simulations.

With its numerous hands-on examples, exercises, and software applications, "Using the Weibull Distribution "is an excellent book for courses on quality control and reliability" "engineering at the upper-undergraduate and graduate levels. The book also serves as a" "valuable reference for engineers, scientists, and business analysts who gather and interpret" "data that follows the Weibull distribution

This book discusses diverse concepts and notions - and their applications - concerning probability and random variables at the intermediate to advanced level. It explains basic concepts and results in a clearer and more complete manner than the extant literature. In addition to a range of concepts and notions concerning probability and random variables, the coverage includes a number of key advanced concepts in mathematics. Readers will also find unique results on e.g. the explicit general formula of joint moments and the expected values of nonlinear functions for normal random vectors. In addition, interesting applications of the step and impulse functions in discussions on random vectors are presented. Thanks to a wealth of examples and a total of 330 practice problems of varying difficulty, readers will have the opportunity to significantly expand their knowledge and skills. The book is rounded out by an extensive index, allowing readers to quickly and easily find what they are looking for. Given its scope, the book will appeal to all readers with a basic grasp of probability and random variables who are looking to go one step further. It also offers a valuable reference guide for experienced scholars and professionals, helping them review and refine their expertise.

Statistical learning and analysis techniques have become extremely important today, given the tremendous growth in the size of heterogeneous data collections and the ability to process it even from physically distant locations. Recent advances made in the field of machine learning provide a strong framework for robust learning from the diverse corpora and continue to impact a variety of research problems across multiple scientific disciplines. The aim of this handbook is to familiarize beginners as well as experts with some of the recent techniques in this field.

The Handbook is divided in two sections: Theory and Applications, covering machine learning, data analytics, biometrics, document recognition and security.
very relevant to current research challenges faced in various fieldsself-contained reference to machine learning

emphasis on applications-oriented techniques

Markov chains are a fundamental class of stochastic processes. They are widely used to solve problems in a large number of domains such as operational research, computer science, communication networks and manufacturing systems. The success of Markov chains is mainly due to their simplicity of use, the large number of available theoretical results and the quality of algorithms developed for the numerical evaluation of many metrics of interest. The author presents the theory of both discrete-time and continuous-time homogeneous Markov chains. He carefully examines the explosion phenomenon, the Kolmogorov equations, the convergence to equilibrium and the passage time distributions to a state and to a subset of states. These results are applied to birth-and-death processes. He then proposes a detailed study of the uniformization technique by means of Banach algebra. This technique is used for the transient analysis of several queuing systems. Contents 1. Discrete-Time Markov Chains 2. Continuous-Time Markov Chains 3. Birth-and-Death Processes 4. Uniformization 5. Queues About the Authors Bruno Sericola is a Senior Research Scientist at Inria Rennes Bretagne Atlantique in France. His main research activity is in performance evaluation of computer and communication systems, dependability analysis of fault-tolerant systems and stochastic models.

The field of statistics not only affects all areas of scientific activity, but also many other matters such as public policy. It is branching rapidly into so many different subjects that a series of handbooks is the only way of comprehensively presenting the various aspects of statistical methodology, applications, and recent developments. The "Handbook of Statistics" is a series of self-contained reference books. Each volume is devoted to a particular topic in statistics, with Volume 30 dealing with time series. The series is addressed to the entire community of statisticians and scientists in various disciplines who use statistical methodology in their work. At the same time, special emphasis is placed on applications-oriented techniques, with the applied statistician in mind as the primary audience.

Comprehensively presents the various aspects of statistical methodologyDiscusses a wide variety of diverse applications and recent developmentsContributors are internationally renowened experts in their respective areas

Students in the sciences, economics, social sciences, and medicine take an introductory statistics course. And yet statistics can be notoriously difficult for instructors to teach and for students to learn. To help overcome these challenges, Gelman and Nolan have put together this fascinating and thought-provoking book. Based on years of teaching experience the book provides a wealth of demonstrations, activities, examples, and projects that involve active student participation. Part I of the book presents a large selection of activities for introductory statistics courses and has chapters such as 'First week of class'- with exercises to break the ice and get students talking; then descriptive statistics, graphics, linear regression, data collection (sampling and experimentation), probability, inference, and statistical communication. Part II gives tips on what works and what doesn't, how to set up effective demonstrations, how to encourage students to participate in class and to work effectively in group projects. Course plans for introductory statistics, statistics for social scientists, and communication and graphics are provided. Part III presents material for more advanced courses on topics such as decision theory, Bayesian statistics, sampling, and data science.

This book shows that research contributions from different fields-finance, economics, computer sciences, and physics-can provide useful insights into key issues in financial and cryptocurrency markets. Presenting the latest empirical and theoretical advances, it helps readers gain a better understanding of financial markets and cryptocurrencies. Bitcoin was the first cryptocurrency to use a peer-to-peer network to prevent double-spending and to control its issue without the need for a central authority, and it has attracted wide public attention since its introduction. In recent years, the academic community has also started gaining interest in cyptocurrencies, and research in the field has grown rapidly. This book presents is a collection of the latest work on cryptocurrency markets and the properties of those markets. This book will appeal to graduate students and researchers from disciplines such as finance, economics, financial engineering, computer science, physics and applied mathematics working in the field of financial markets, including cryptocurrency markets.

This book describes methods for statistical brain imaging data analysis from both the perspective of methodology and from the standpoint of application for software implementation in neuroscience research. These include those both commonly used (traditional established) and state of the art methods. The former is easier to do due to the availability of appropriate software. To understand the methods it is necessary to have some mathematical knowledge which is explained in the book with the help of figures and descriptions of the theory behind the software. In addition, the book includes numerical examples to guide readers on the working of existing popular software. The use of mathematics is reduced and simplified for non-experts using established methods, which also helps in avoiding mistakes in application and interpretation. Finally, the book enables the reader to understand and conceptualize the overall flow of brain imaging data analysis, particularly for statisticians and data-scientists unfamiliar with this area. The state of the art method described in the book has a multivariate approach developed by the authors' team. Since brain imaging data, generally, has a highly correlated and complex structure with large amounts of data, categorized into big data, the multivariate approach can be used as dimension reduction by following the application of statistical methods. The R package for most of the methods described is provided in the book. Understanding the background theory is helpful in implementing the software for original and creative applications and for an unbiased interpretation of the output. The book also explains new methods in a conceptual manner. These methodologies and packages are commonly applied in life science data analysis. Advanced methods to obtain novel insights are introduced, thereby encouraging the development of new methods and applications for research into medicine as a neuroscience.

This accessible reference includes selected contributions from Bayesian Thinking - Modeling and Computation, Volume 25 in the Handbook of Statistics Series, with a focus on key methodologies and applications for Bayesian models and computation. It describes parametric and nonparametric Bayesian methods for modeling, and how to use modern computational methods to summarize inferences using simulation. The book covers a wide range of topics including objective and subjective Bayesian inferences, with a variety of applications in modeling categorical, survival, spatial, spatiotemporal, Epidemiological, small area and micro array data.

Aids critical thinking on causal effects
Provides simulation based computing techniques
Covers Bioinformatics and Biostatistics

Chance rules our daily lives in many different ways. From the outcomes of the lottery to the outcomes of medical tests, from the basketball court to the court of law. The ways of chance are capricious. Bizarre things happen all the time. Nevertheless, chance has a logic of its own. It obeys the rules of probability. But if you open a standard book on probability, you may very well feel far removed from everyday life. Abstract formulas and mathematical symbols stare back at you with almost every turn of the page.This book introduces you to the logic of chance without the use of mathematical formulas or symbols. In Part One, you will meet the fascinating pioneers of the mathematics of probability, including Galileo Galilei and Blaise Pascal. Their stories will introduce you, step by step, to the basics of probability. In Part Two, various examples in all areas of daily life will show you how chance defies our expectations time and again. But armed with the basic rules of probability and a good dose of inventiveness, you will be able to unravel the counter-intuitive logic of chance.

Praise for the First Edition

" . . . an excellent addition to an upper-level undergraduate course on environmental statistics, and . . . a 'must-have' desk reference for environmental practitioners dealing with censored datasets."
--Vadose Zone Journal

Statistical Methods for Censored Environmental Data Using Minitab(R) and R, Second Edition introduces and explains methods for analyzing and interpreting censored data in the environmental sciences. Adapting survival analysis techniques from other fields, the book translates well-established methods from other disciplines into new solutions for environmental studies.

This new edition applies methods of survival analysis, including methods for interval-censored data to the interpretation of low-level contaminants in environmental sciences and occupational health. Now incorporating the freely available R software as well as Minitab(R) into the discussed analyses, the book features newly developed and updated material including:

A new chapter on multivariate methods for censored data

Use of interval-censored methods for treating true nondetects as lower than and separate from values between the detection and quantitation limits ("remarked data")

A section on summing data with nondetects

A newly written introduction that discusses invasive data, showing why substitution methods fail

Expanded coverage of graphical methods for censored data

The author writes in a style that focuses on applications rather than derivations, with chapters organized by key objectives such as computing intervals, comparing groups, and correlation. Examples accompany each procedure, utilizing real-world data that can be analyzed using the Minitab(R) and R software macros available on the book's related website, and extensive references direct readers to authoritative literature from the environmental sciences.

Statistics for Censored Environmental Data Using Minitab(R) and R, Second Edition is an excellent book for courses on environmental statistics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for?environmental professionals, biologists, and ecologists who focus on the water sciences, air quality, and soil science.

This book bridges theoretical computer science and machine learning by exploring what the two sides can teach each other. It emphasizes the need for flexible, tractable models that better capture not what makes machine learning hard, but what makes it easy. Theoretical computer scientists will be introduced to important models in machine learning and to the main questions within the field. Machine learning researchers will be introduced to cutting-edge research in an accessible format, and gain familiarity with a modern, algorithmic toolkit, including the method of moments, tensor decompositions and convex programming relaxations. The treatment beyond worst-case analysis is to build a rigorous understanding about the approaches used in practice and to facilitate the discovery of exciting, new ways to solve important long-standing problems.

Using Bishop's work on constructive analysis as a framework, this monograph gives a systematic, detailed and general constructive theory of probability theory and stochastic processes. It is the first extended account of this theory: almost all of the constructive existence and continuity theorems that permeate the book are original. It also contains results and methods hitherto unknown in the constructive and nonconstructive settings. The text features logic only in the common sense and, beyond a certain mathematical maturity, requires no prior training in either constructive mathematics or probability theory. It will thus be accessible and of interest, both to probabilists interested in the foundations of their speciality and to constructive mathematicians who wish to see Bishop's theory applied to a particular field.

This new handbook contains the most comprehensive account of sample surveys theory and practice to date. It is a second volume on sample surveys, with the goal of updating and extending the sampling volume published as volume 6 of the Handbook of Statistics in 1988. The present handbook is divided into two volumes (29A and 29B), with a total of 41 chapters, covering current developments in almost every aspect of sample surveys, with references to important contributions and available software. It can serve as a self contained guide to researchers and practitioners, with appropriate balance between theory and real life applications.

Each of the two volumes is divided into three parts, with each part preceded by an introduction, summarizing the main developments in the areas covered in that part. Volume29A deals with methods of sample selection and data processing, with the later including editing and imputation, handling of outliers and measurement errors, and methods of disclosure control. The volume contains also a large variety of applications in specialized areas such as household and business surveys, marketing research, opinion polls and censuses. Volume29B is concerned with inference, distinguishing between design-based and model-based methods and focusing on specific problems such as small area estimation, analysis of longitudinal data, categorical data analysis and inference on distribution functions. The volume contains also chapters dealing with case-control studies, asymptotic properties of estimators and decision theoretic aspects.
Comprehensive account of recent developments in sample survey theory and practiceDiscussesa wide variety of diverse applicationsComprehensive bibliography"

Congruences are ubiquitous in computer science, engineering, mathematics, and related areas. Developing techniques for finding (the number of) solutions of congruences is an important problem. But there are many scenarios in which we are interested in only a subset of the solutions; in other words, there are some restrictions. What do we know about these restricted congruences, their solutions, and applications? This book introduces the tools that are needed when working on restricted congruences and then systematically studies a variety of restricted congruences. Restricted Congruences in Computing defines several types of restricted congruence, obtains explicit formulae for the number of their solutions using a wide range of tools and techniques, and discusses their applications in cryptography, information security, information theory, coding theory, string theory, quantum field theory, parallel computing, artificial intelligence, computational biology, discrete mathematics, number theory, and more. This is the first book devoted to restricted congruences and their applications. It will be of interest to graduate students and researchers across computer science, electrical engineering, and mathematics.

This new handbook contains the most comprehensive account of sample surveys theory and practice to date. It is a second volume on sample surveys, with the goal of updating and extending the sampling volume published as volume 6 of the Handbook of Statistics in 1988. The present handbook is divided into two volumes (29A and 29B), with a total of 41 chapters, covering current developments in almost every aspect of sample surveys, with references to important contributions and available software. It can serve as a self contained guide to researchers and practitioners, with appropriate balance between theory and real life applications.

Each of the two volumes is divided into three parts, with each part preceded by an introduction, summarizing the main developments in the areas covered in that part. Volume 1 deals with methods of sample selection and data processing, with the later including editing and imputation, handling of outliers and measurement errors, and methods of disclosure control. The volume contains also a large variety of applications in specialized areas such as household and business surveys, marketing research, opinion polls and censuses. Volume 2 is concerned with inference, distinguishing between design-based and model-based methods and focusing on specific problems such as small area estimation, analysis of longitudinal data, categorical data analysis and inference on distribution functions. The volume contains also chapters dealing with case-control studies, asymptotic properties of estimators and decision theoretic aspects.

Comprehensive account of recent developments in sample survey theory and practice

Covers a wide variety of diverse applications

Comprehensive bibliography

Bayesian analysis has developed rapidly in applications in the last two decades and research in Bayesian methods remains dynamic and fast-growing. Dramatic advances in modelling concepts and computational technologies now enable routine application of Bayesian analysis using increasingly realistic stochastic models, and this drives the adoption of Bayesian approaches in many areas of science, technology, commerce, and industry.
This Handbook explores contemporary Bayesian analysis across a variety of application areas. Chapters written by leading exponents of applied Bayesian analysis showcase the scientific ease and natural application of Bayesian modelling, and present solutions to real, engaging, societally important and demanding problems. The chapters are grouped into five general areas: Biomedical & Health Sciences; Industry, Economics & Finance; Environment & Ecology; Policy, Political & Social Sciences; and Natural & Engineering Sciences, and Appendix material in each touches on key concepts, models, and techniques of the chapter that are also of broader pedagogic and applied interest.

Peter Goos, Department of Statistics, University of Leuven, Faculty of Bio-Science Engineering and University of Antwerp, Faculty of Applied Economics, Belgium David Meintrup, Department of Mathematics and Statistics, University of Applied Sciences Ingolstadt, Faculty of Mechanical Engineering, Germany Thorough presentation of introductory statistics and probability theory, with numerous examples and applications using JMP JMP: Graphs, Descriptive Statistics and Probability provides an accessible and thorough overview of the most important descriptive statistics for nominal, ordinal and quantitative data with particular attention to graphical representations. The authors distinguish their approach from many modern textbooks on descriptive statistics and probability theory by offering a combination of theoretical and mathematical depth, and clear and detailed explanations of concepts. Throughout the book, the user-friendly, interactive statistical software package JMP is used for calculations, the computation of probabilities and the creation of figures. The examples are explained in detail, and accompanied by step-by-step instructions and screenshots. The reader will therefore develop an understanding of both the statistical theory and its applications. Traditional graphs such as needle charts, histograms and pie charts are included, as well as the more modern mosaic plots, bubble plots and heat maps. The authors discuss probability theory, particularly discrete probability distributions and continuous probability densities, including the binomial and Poisson distributions, and the exponential, normal and lognormal densities. They use numerous examples throughout to illustrate these distributions and densities. Key features: * Introduces each concept with practical examples and demonstrations in JMP. * Provides the statistical theory including detailed mathematical derivations. * Presents illustrative examples in each chapter accompanied by step-by-step instructions and screenshots to help develop the reader s understanding of both the statistical theory and its applications. * A supporting website with data sets and other teaching materials. This book is equally aimed at students in engineering, economics and natural sciences who take classes in statistics as well as at masters/advanced students in applied statistics and probability theory. For teachers of applied statistics, this book provides a rich resource of course material, examples and applications.

Economic theories can be expressed in words, numbers, graphs and symbols. The existing traditional economics textbooks cover all four methods, but the general focus is often more on writing about the theory and methods, with few practical examples. With an increasing number of universities having introduced mathematical economics at undergraduate level, Basic mathematics for economic students aims to fill this gap in the field. Basic mathematics for economic students begins with a comprehensive chapter on basic mathematical concepts and methods (suitable for self-study, revision or tutorial purposes) to ensure that students have the necessary foundation. The book is written in an accessible style and is extremely practical. Numerous mathematical economics examples and exercises are provided as well as fully worked solutions using numbers, graphs and symbols. Basic mathematics for economic students is aimed at all economics students. It focuses on quantitative aspects and especially complements the two highly popular theoretical economics textbooks Understanding microeconomics and Understanding macroeconomics, both written by Philip Mohr and published by Van Schaik.