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Heavy-tailed distributions are typical for phenomena in complex multi-component systems such as biometry, economics, ecological systems, sociology, web access statistics, internet traffic, biblio-metrics, finance and business. The analysis of such distributions requires special methods of estimation due to their specific features. These are not only the slow decay to zero of the tail, but also the violation of Cramer’s condition, possible non-existence of some moments, and sparse observations in the tail of the distribution. The book focuses on the methods of statistical analysis of heavy-tailed independent identically distributed random variables by empirical samples of moderate sizes. It provides a detailed survey of classical results and recent developments in the theory of nonparametric estimation of the probability density function, the tail index, the hazard rate and the renewal function. Both asymptotical results, for example convergence rates of the estimates, and results for the samples of moderate sizes supported by Monte-Carlo investigation, are considered. The text is illustrated by the application of the considered methodologies to real data of web traffic measurements.
Twenty-four contributions, intended for a wide audience from various disciplines, cover a variety of applications of heavy-tailed modeling involving telecommunications, the Web, insurance, and finance. Along with discussion of specific applications are several papers devoted to time series analysis, regression, classical signal/noise detection problems, and the general structure of stable processes, viewed from a modeling standpoint. Emphasis is placed on developments in handling the numerical problems associated with stable distribution (a main technical difficulty until recently). No index. Annotation copyrighted by Book News, Inc., Portland, OR
Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterious, surprising, and even controversial, primarily because the necessary mathematical models and statistical methods are not widely known. This book, for the first time, provides a rigorous introduction to heavy-tailed distributions accessible to anyone who knows elementary probability. It tackles and tames the zoo of terminology for models and properties, demystifying topics such as the generalized central limit theorem and regular variation. It tracks the natural emergence of heavy-tailed distributions from a wide variety of general processes, building intuition. And it reveals the controversy surrounding heavy tails to be the result of flawed statistics, then equips readers to identify and estimate with confidence. Over 100 exercises complete this engaging package.
Theories and practices to assess critical information in a complex adaptive system Organized for readers to follow along easily, The Fitness of Information: Quantitative Assessments of Critical Evidence provides a structured outline of the key challenges in assessing crucial information in a complex adaptive system. Illustrating a variety of computational and explanatory challenges, the book demonstrates principles and practical implications of exploring and assessing the fitness of information in an extensible framework of adaptive landscapes. The book’s first three chapters introduce fundamental principles and practical examples in connection to the nature of aesthetics, mental models, and the subjectivity of evidence. In particular, the underlying question is how these issues can be addressed quantitatively, not only computationally but also explanatorily. The next chapter illustrates how one can reduce the level of complexity in understanding the structure and dynamics of scientific knowledge through the design and use of the CiteSpace system for visualizing and analyzing emerging trends in scientific literature. The following two chapters explain the concepts of structural variation and the fitness of information in a framework that builds on the idea of fitness landscape originally introduced to study population evolution. The final chapter presents a dual-map overlay technique and demonstrates how it supports a variety of analytic tasks for a new type of portfolio analysis. The Fitness of Information: Quantitative Assessments of Critical Evidence also features: In-depth case studies and examples that characterize far-reaching concepts, illustrate underlying principles, and demonstrate profound challenges and complexities at various levels of analytic reasoning Wide-ranging topics that underline the common theme, from the subjectivity of evidence in criminal trials to detecting early signs of critical transitions and mechanisms behind radical patents An extensible and unifying framework for visual analytics by transforming analytic reasoning tasks to the assessment of critical evidence The Fitness of Information: Quantitative Assessments of Critical Evidence is a suitable reference for researchers, analysts, and practitioners who are interested in analyzing evidence and making decisions with incomplete, uncertain, and even conflicting information. The book is also an excellent textbook for upper-undergraduate and graduate-level courses on visual analytics, information visualization, and business analytics and decision support systems.
An up-to-date version of the complete, self-contained introduction to matrix analysis theory and practice Providing accessible and in-depth coverage of the most common matrix methods now used in statistical applications, Matrix Analysis for Statistics, Third Edition features an easy-to-follow theorem/proof format. Featuring smooth transitions between topical coverage, the author carefully justifies the step-by-step process of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors; the Moore-Penrose inverse; matrix differentiation; and the distribution of quadratic forms. An ideal introduction to matrix analysis theory and practice, Matrix Analysis for Statistics, Third Edition features: • New chapter or section coverage on inequalities, oblique projections, and antieigenvalues and antieigenvectors • Additional problems and chapter-end practice exercises at the end of each chapter • Extensive examples that are familiar and easy to understand • Self-contained chapters for flexibility in topic choice • Applications of matrix methods in least squares regression and the analyses of mean vectors and covariance matrices Matrix Analysis for Statistics, Third Edition is an ideal textbook for upper-undergraduate and graduate-level courses on matrix methods, multivariate analysis, and linear models. The book is also an excellent reference for research professionals in applied statistics. James R. Schott, PhD, is Professor in the Department of Statistics at the University of Central Florida. He has published numerous journal articles in the area of multivariate analysis. Dr. Schott’s research interests include multivariate analysis, analysis of covariance and correlation matrices, and dimensionality reduction techniques.
Bayesian analysis of complex models based on stochastic processes has in recent years become a growing area. This book provides a unified treatment of Bayesian analysis of models based on stochastic processes, covering the main classes of stochastic processing including modeling, computational, inference, forecasting, decision making and important applied models. Key features: Explores Bayesian analysis of models based on stochastic processes, providing a unified treatment. Provides a thorough introduction for research students. Computational tools to deal with complex problems are illustrated along with real life case studies Looks at inference, prediction and decision making. Researchers, graduate and advanced undergraduate students interested in stochastic processes in fields such as statistics, operations research (OR), engineering, finance, economics, computer science and Bayesian analysis will benefit from reading this book. With numerous applications included, practitioners of OR, stochastic modelling and applied statistics will also find this book useful.
Praise for the First Edition "…[t]he book is great for readers who need to applythe methods and models presented but have little background inmathematics and statistics." -MAA Reviews Thoroughly updated throughout, Introduction to Time SeriesAnalysis and Forecasting, Second Edition presents theunderlying theories of time series analysis that are needed toanalyze time-oriented data and construct real-world short- tomedium-term statistical forecasts. Authored by highly-experienced academics and professionals inengineering statistics, the Second Edition featuresdiscussions on both popular and modern time series methodologies aswell as an introduction to Bayesian methods in forecasting.Introduction to Time Series Analysis and Forecasting, SecondEdition also includes: Over 300 exercises from diverse disciplines including healthcare, environmental studies, engineering, and finance More than 50 programming algorithms using JMP®, SAS®,and R that illustrate the theory and practicality of forecastingtechniques in the context of time-oriented data New material on frequency domain and spatial temporaldata analysis Expanded coverage of the variogram and spectrum withapplications as well as transfer and intervention modelfunctions A supplementary website featuring PowerPoint®slides, data sets, and select solutions to the problems Introduction to Time Series Analysis and Forecasting, SecondEdition is an ideal textbook upper-undergraduate andgraduate-levels courses in forecasting and time series. The book isalso an excellent reference for practitioners and researchers whoneed to model and analyze time series data to generate forecasts.
This book constitutes the refereed post-conference proceedings of the 25th International Conference on Distributed and Computer and Communication Networks, DCCN 2022, held in Moscow, Russia, in September 26–29, 2022. The 31 revised full papers and 2 revised short papers were carefully reviewed and selected from 130 submissions. The papers cover the following topics: computer and communication networks; analytical modeling of distributed systems; and distributed systems applications.
This volume presents the latest advances and trends in nonparametric statistics, and gathers selected and peer-reviewed contributions from the 3rd Conference of the International Society for Nonparametric Statistics (ISNPS), held in Avignon, France on June 11-16, 2016. It covers a broad range of nonparametric statistical methods, from density estimation, survey sampling, resampling methods, kernel methods and extreme values, to statistical learning and classification, both in the standard i.i.d. case and for dependent data, including big data. The International Society for Nonparametric Statistics is uniquely global, and its international conferences are intended to foster the exchange of ideas and the latest advances among researchers from around the world, in cooperation with established statistical societies such as the Institute of Mathematical Statistics, the Bernoulli Society and the International Statistical Institute. The 3rd ISNPS conference in Avignon attracted more than 400 researchers from around the globe, and contributed to the further development and dissemination of nonparametric statistics knowledge.
An essential resource for constructing and analyzing advanced actuarial models Loss Models: Further Topics presents extended coverage of modeling through the use of tools related to risk theory, loss distributions, and survival models. The book uses these methods to construct and evaluate actuarial models in the fields of insurance and business. Providing an advanced study of actuarial methods, the book features extended discussions of risk modeling and risk measures, including Tail-Value-at-Risk. Loss Models: Further Topics contains additional material to accompany the Fourth Edition of Loss Models: From Data to Decisions, such as: Extreme value distributions Coxian and related distributions Mixed Erlang distributions Computational and analytical methods for aggregate claim models Counting processes Compound distributions with time-dependent claim amounts Copula models Continuous time ruin models Interpolation and smoothing The book is an essential reference for practicing actuaries and actuarial researchers who want to go beyond the material required for actuarial qualification. Loss Models: Further Topics is also an excellent resource for graduate students in the actuarial field.