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Copulas are functions that join multivariate distribution functions to their one-dimensional margins. The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. With nearly a hundred examples and over 150 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. Roger B. Nelsen is Professor of Mathematics at Lewis & Clark College in Portland, Oregon. He is also the author of "Proofs Without Words: Exercises in Visual Thinking," published by the Mathematical Association of America.

Proofs without words (PWWs) are figures or diagrams that help the reader see why a particular mathematical statement is true, and how one might begin to formally prove it true. PWWs are not new, many date back to classical Greece, ancient China, and medieval Europe and the Middle East. PWWs have been regular features of the MAA journals Mathematics Magazine and The College Mathematics Journal for many years, and the MAA published the collections of PWWs Proofs Without Words: Exercises in Visual Thinking in 1993 and Proofs Without Words II: More Exercises in Visual Thinking in 2000. This book is the third such collection of PWWs.

A collection of remarkable proofs that are exceptionally elegant, and thus invite the reader to enjoy the beauty of mathematics.

This book presents contributions and review articles on the theory of copulas and their applications. The authoritative and refereed contributions review the latest findings in the area with emphasis on “classical” topics like distributions with fixed marginals, measures of association, construction of copulas with given additional information, etc. The book celebrates the 75th birthday of Professor Roger B. Nelsen and his outstanding contribution to the development of copula theory. Most of the book’s contributions were presented at the conference “Copulas and Their Applications” held in his honor in Almería, Spain, July 3-5, 2017. The chapter 'When Gumbel met Galambos' is published open access under a CC BY 4.0 license.

This volume gives a state of the art of triangular norms which can be used for the generalization of several mathematical concepts, such as conjunction, metric, measure, etc. 16 chapters written by leading experts provide a state of the art overview of theory and applications of triangular norms and related operators in fuzzy logic, measure theory, probability theory, and probabilistic metric spaces. Key Features: - Complete state of the art of the importance of triangular norms in various mathematical fields - 16 self-contained chapters with extensive bibliographies cover both the theoretical background and many applications - Chapter authors are leading authorities in their fields - Triangular norms on different domains (including discrete, partially ordered) are described - Not only triangular norms but also related operators (aggregation operators, copulas) are covered - Book contains many enlightening illustrations · Complete state of the art of the importance of triangular norms in various mathematical fields · 16 self-contained chapters with extensive bibliographies cover both the theoretical background and many applications · Chapter authors are leading authorities in...

Being the premier forum for the presentation of new advances and research results in the fields of Industrial Engineering, IEEM 2014 aims to provide a high-level international forum for experts, scholars and entrepreneurs at home and abroad to present the recent advances, new techniques and applications face and face, to promote discussion and interaction among academics, researchers and professionals to promote the developments and applications of the related theories and technologies in universities and enterprises and to establish business or research relations to find global partners for future collaboration in the field of Industrial Engineering. All the goals of the international conference are to fulfill the mission of the series conference which is to review, exchange, summarize and promote the latest achievements in the field of industrial engineering and engineering management over the past year and to propose prospects and vision for the further development.

The field of Information Systems has been shifting from an aeimmersion viewAE, which relies on the immersion of information technology (IT) as part of the business environment, to a aefusion viewAE in which IT is fused within the business environment, forming a unified fabric that integrates work and personal life, as well as personal and public information. In the context of this fusion view, decision support systems should achieve a total alignment with the context and the personal preferences of users. The advantage of such a view is an opportunity of seamless integration between enterprise environments and decision support system components. Thus, researchers and practitioners have to address the challenges of dealing with this shift in viewpoint and its consequences for decision making and decision support systems theories and applications. This book presents the latest innovations and advances in decision support systems with a special focus on the fusion view. These achievements will be of interest to all those involved and interested in decision making practice and research, as well as, more generally, in the fusion view of modern information systems.The book covers a wide ...

This volume contains the papers presented at the meeting "Distributions with given marginals and statistical modelling", held in Barcelona (Spain), July 17- 20, 2000. This is the fourth meeting on given marginals, showing that this topic has aremarkable interest. BRIEF HISTORY The construction of distributions with given marginals started with the seminal papers by Hoeffding (1940) and Fn!chet (1951). Since then, many others have contributed on this topic: Dall' Aglio, Farlie, Gumbel, Johnson, Kellerer, Kotz, Morgenstern, Marshali, Olkin, Strassen, Vitale, Whitt, etc., as weIl as Arnold, Cambanis, Deheuvels, Genest, Frank, Joe, Kirneldorf, Nelsen, Rüschendorf, Sampson, Scarsini, Tiit, etc. In 1957 Sklar and Schweizer introduced probabilistic metric spaces. In 1975 Kirneldorf and Sampson studied the uniform representation of a bivariate dis tribution and proposed the desirable conditions that should be satisfied by any bivariate family. In 1991 Darsow, Nguyen and Olsen defined a natural operation between cop ulas, with applications in stochastic processes. In 1993, AIsina, Nelsen and Schweizer introduced the notion of quasi-copula

Mathematics of the Financial Markets Financial Instruments and Derivatives Modeling, Valuation and Risk Issues "Alain Ruttiens has the ability to turn extremely complex concepts and theories into very easy to understand notions. I wish I had read his book when I started my career!" Marco Dion, Global Head of Equity Quant Strategy, J.P. Morgan "The financial industry is built on a vast collection of financial securities that can be valued and risk profiled using a set of miscellaneous mathematical models. The comprehension of these models is fundamental to the modern portfolio and risk manager in order to achieve a deep understanding of the capabilities and limitations of these methods in the approximation of the market. In his book, Alain Ruttiens exposes these models for a wide range of financial instruments by using a detailed and user friendly approach backed up with real-life data examples. The result is an excellent entry-level and reference book that will help any student and current practitioner up their mathematical modeling skills in the increasingly demanding domain of asset and risk management." Virgile Rostand, Consultant, Toronto ON "Alain Ruttiens not only presents...

The International Symposium on Dynamics of Vehicles on Roads and Tracks is the leading international gathering of scientists and engineers from academia and industry in the field of ground vehicle dynamics to present and exchange their latest innovations and breakthroughs. Established in Vienna in 1977, the International Association of Vehicle System Dynamics (IAVSD) has since held its biennial symposia throughout Europe and in the USA, Canada, Japan, South Africa and China. The main objectives of IAVSD are to promote the development of the science of vehicle dynamics and to encourage engineering applications of this field of science, to inform scientists and engineers on the current state-of-the-art in the field of vehicle dynamics and to broaden contacts among persons and organisations of the various countries engaged in scientific research and development in the field of vehicle dynamics and related areas. IAVSD 2017, the 25th Symposium of the International Association of Vehicle System Dynamics was hosted by the Centre for Railway Engineering at Central Queensland University, Rockhampton, Australia in August 2017. The symposium focused on the following topics related to road...

This book rehabilitates beta as a definition of systemic risk by using particle physics to evaluate discrete components of financial risk. Much of the frustration with beta stems from the failure to disaggregate its discrete components; conventional beta is often treated as if it were "atomic" in the original Greek sense: uncut and indivisible. By analogy to the Standard Model of particle physics theory's three generations of matter and the three-way interaction of quarks, Chen divides beta as the fundamental unit of systemic financial risk into three matching pairs of "baryonic" components. The resulting econophysics of beta explains no fewer than three of the most significant anomalies and puzzles in mathematical finance. Moreover, the model's three-way analysis of systemic risk connects the mechanics of mathematical finance with phenomena usually attributed to behavioral influences on capital markets. Adding consideration of volatility and correlation, and of the distinct cash flow and discount rate components of systematic risk, harmonizes mathematical finance with labor markets, human capital, and macroeconomics.

This survey of portfolio theory, from its modern origins through more sophisticated, “postmodern” incarnations, evaluates portfolio risk according to the first four moments of any statistical distribution: mean, variance, skewness, and excess kurtosis. In pursuit of financial models that more accurately describe abnormal markets and investor psychology, this book bifurcates beta on either side of mean returns. It then evaluates this traditional risk measure according to its relative volatility and correlation components. After specifying a four-moment capital asset pricing model, this book devotes special attention to measures of market risk in global banking regulation. Despite the deficiencies of modern portfolio theory, contemporary finance continues to rest on mean-variance optimization and the two-moment capital asset pricing model. The term postmodern portfolio theory captures many of the advances in financial learning since the original articulation of modern portfolio theory. A comprehensive approach to financial risk management must address all aspects of portfolio theory, from the beautiful symmetries of modern portfolio theory to the disturbing behavioral insights...

The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces. The necessary mathematical tools are presented in Chapters 1 and 2. Chapters 3 to 6 deal with autoregressive processes in Hilbert and Banach spaces. Chapter 7 is devoted to general linear processes and Chapter 8 with statistical prediction. Implementation and numerical applications appear in Chapter 9. The book assumes a knowledge of classical probability theory and statistics. Denis Bosq is Professor of Statistics at the University of Paris 6 (Pierre et Marie Curie). He is Chief-Editor of Statistical Inference for Stochastic Processes and of Annales de l'ISUP, and Associate Editor of the Journal of Nonparametric Statistics. He is an elected member of the International Statistical Institute, and he has published about 100 papers or works on nonparametric statistics and five books including Nonparametric Statistics for Stochastic Processes: Estimation and Prediction, Second Edition (Springer, 1998).

This book presents a unified approach for obtaining the limiting distributions of minimum distance. It discusses classes of goodness-of-t tests for fitting an error distribution in some of these models and/or fitting a regression-autoregressive function without assuming the knowledge of the error distribution. The main tool is the asymptotic equi-continuity of certain basic weighted residual empirical processes in the uniform and L2 metrics.

There are two main problems in statistics, estimation theory and hypothesis testing. For the classical finite-parametric case, these problems were studied in parallel. On the other hand, many statistical problems are not parametric in the classical sense; the objects of estimation or testing are functions, images, and so on. These can be treated as unknown infinite-dimensional parameters that belong to specific functional sets. This approach to nonparametric estimation under asymptotically minimax setting was started in the 1960s-1970s and was developed very intensively for wide classes of functional sets and loss functions. Nonparametric estimation problems have generated a large literature. On the other hand, nonparametric hypotheses testing problems have not drawn comparable attention in the statistical literature. In this book, the authors develop a modern theory of nonparametric goodness-of-fit testing. The presentation is based on an asymptotic version of the minimax approach. The key element of the theory is the method of constructing of asymptotically least favorable priors for a wide enough class of nonparametric hypothesis testing problems. These provide methods for the...

This volume shows how sophisticated spatial statistical and computational methods apply to a range of problems of increasing importance for applications in science and technology. It introduces topics of current interest in spatial and computational statistics, which should be accessible to postgraduate students as well as to experienced statistical researchers.

These notes represent our summary of much of the recent research that has been done in recent years on approximations and bounds that have been developed for compound distributions and related quantities which are of interest in insurance and other areas of application in applied probability. The basic technique employed in the derivation of many bounds is induc tive, an approach that is motivated by arguments used by Sparre-Andersen (1957) in connection with a renewal risk model in insurance. This technique is both simple and powerful, and yields quite general results. The bounds themselves are motivated by the classical Lundberg exponential bounds which apply to ruin probabilities, and the connection to compound dis tributions is through the interpretation of the ruin probability as the tail probability of a compound geometric distribution. The initial exponential bounds were given in Willmot and Lin (1994), followed by the nonexpo nential generalization in Willmot (1994). Other related work on approximations for compound distributions and applications to various problems in insurance in particular and applied probability in general is also discussed in subsequent chapters. The...

Bayesian and such approaches to inference have a number of points of close contact, especially from an asymptotic point of view. Both emphasize the construction of interval estimates of unknown parameters. In this volume, researchers present recent work on several aspects of Bayesian, likelihood and empirical Bayes methods, presented at a workshop held in Montreal, Canada. The goal of the workshop was to explore the linkages among the methods, and to suggest new directions for research in the theory of inference.

This is the first book on the topic of probability matching priors. It targets researchers, Bayesian and frequentist; graduate students in Statistics.

Time series play a crucial role in modern economies at all levels of activity and are used by decision makers to plan for a better future. Before publication time series are subject to statistical adjustments and this is the first statistical book to systematically deal with the methods most often applied for such adjustments. Regression-based models are emphasized because of their clarity, ease of application, and superior results. Each topic is illustrated with real case examples. In order to facilitate understanding of their properties and limitations of the methods discussed a real data example is followed throughout the book.

This volume contains invited case studies with the accompanying discussion as well as contributed papers selected by a refereeing process of 6th Workshop on Case Studies in Bayesian Statistics was held at the Carnegie Mellon University in October, 2001.

Monte Carlo approximation to the null distribution of the test provides a convenient means of testing model fit. This book proposes a Monte Carlo-based methodology to construct this type of approximation when the model is semistructured. It addresses both applied and theoretical aspects of nonparametric Monte Carlo tests.

In his seminal 1982 paper, Robert F. Engle described a time series model with a time-varying volatility. Engle showed that this model, which he called ARCH (autoregressive conditionally heteroscedastic), is well-suited for the description of economic and financial price. Nowadays ARCH has been replaced by more general and more sophisticated models, such as GARCH (generalized autoregressive heteroscedastic). This monograph concentrates on mathematical statistical problems associated with fitting conditionally heteroscedastic time series models to data. This includes the classical statistical issues of consistency and limiting distribution of estimators. Particular attention is addressed to (quasi) maximum likelihood estimation and misspecified models, along to phenomena due to heavy-tailed innovations. The used methods are based on techniques applied to the analysis of stochastic recurrence equations. Proofs and arguments are given wherever possible in full mathematical rigour. Moreover, the theory is illustrated by examples and simulation studies.

By providing a comprehensive look at statistical inference from record-breaking data in both parametric and nonparametric settings, this book treats the area of nonparametric function estimation from such data in detail. Its main purpose is to fill this void on general inference from record values. Statisticians, mathematicians, and engineers will find the book useful as a research reference. It can also serve as part of a graduate-level statistics or mathematics course.

This monograph is aimed at developing Doukhan/Louhichi's (1999) idea to measure asymptotic independence of a random process. The authors propose various examples of models fitting such conditions such as stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovian, and heteroskedastic models with infinite memory. Most of the commonly used stationary models fit their conditions. The simplicity of the conditions is also their strength. The main existing tools for an asymptotic theory are developed under weak dependence. They apply the theory to nonparametric statistics, spectral analysis, econometrics, and resampling. The level of generality makes those techniques quite robust with respect to the model. The limit theorems are sometimes sharp and always simple to apply. The theory (with proofs) is developed and the authors propose to fix the notation for future applications. A large number of research papers deals with the present ideas; the authors as well as numerous other investigators participated actively in the development of this theory. Several applications are still needed to develop a method of analysis for (nonlinear) times series and they...

This volume contains presentations by eminent researchers: Statistical Inference for Spatial Processes; Image Analysis; Applications of Spatial Statistics in Earth, Environmental, and Health Sciences; and Statistics of Brain Mapping. They range from asymptotic considerations for spatial processes to practical considerations related to particular applications including important methodological aspects. Many contributions concern image analysis, mainly images related to brain mapping.

This collection of papers provides an up to date treatment of item response theory, an important topic in educational testing.

Government policy questions and media planning tasks may be answered by this data set. It covers a wide range of different aspects of statistical matching that in Europe typically is called data fusion. A book about statistical matching will be of interest to researchers and practitioners, starting with data collection and the production of public use micro files, data banks, and data bases. People in the areas of database marketing, public health analysis, socioeconomic modeling, and official statistics will find it useful.

The first book on the concept and applications of ranked set sampling. It provides a comprehensive review of the literature, and it includes many new results and novel applications. The detailed description of various methods illustrated by real or simulated data makes it useful for scientists and practitioners in application areas such as agriculture, forestry, sociology, ecological and environmental science, and medical studies. It can serve as a reference book and as a textbook for a short course at the graduate level.

The book is composed of two volumes, each consisting of five chapters. In Vol ume I, following some statistical motivation based on a randomization model, a general theory of the analysis of experiments in block designs has been de veloped. In the present Volume II, the primary aim is to present methods of that satisfy the statistical requirements described in constructing block designs Volume I, particularly those considered in Chapters 3 and 4, and also to give some catalogues of plans of the designs. Thus, the constructional aspects are of predominant interest in Volume II, with a general consideration given in Chapter 6. The main design investigations are systematized by separating the material into two contents, depending on whether the designs provide unit efficiency fac tors for some contrasts of treatment parameters (Chapter 7) or not (Chapter 8). This distinction in classifying block designs may be essential from a prac tical point of view. In general, classification of block designs, whether proper or not, is based here on efficiency balance (EB) in the sense of the new termi nology proposed in Section 4. 4 (see, in particular, Definition 4. 4. 2). Most of the attention...

This book is devoted to the study of univariate distributions appropriate for the analyses of data known to be nonnegative. The book includes much material from reliability theory in engineering and survival analysis in medicine.

Solid geometry is the traditional name for what we call today the geometry of three-dimensional Euclidean space. This book presents techniques for proving a variety of geometric results in three dimensions. Special attention is given to prisms, pyramids, platonic solids, cones, cylinders and spheres, as well as many new and classical results. A chapter is devoted to each of the following basic techniques for exploring space and proving theorems: enumeration, representation, dissection, plane sections, intersection, iteration, motion, projection, and folding and unfolding. The book includes a selection of Challenges for each chapter with solutions, references and a complete index. The text is aimed at secondary school and college and university teachers as an introduction to solid geometry, as a supplement in problem solving sessions, as enrichment material in a course on proofs and mathematical reasoning, or in a mathematics course for liberal arts students.--

Collection of selected, peer reviewed papers from the 2013 2nd International Conference on Mechanical Engineering, Industrial Electronics and Informatization (MEIEI 2013), September 14-15, 2013, Chongqing, China. The 656 papers are grouped as follows: Chapter 1: Applied Mechanics and Advances in Mechanical Engineering; Chapter 2: Industrial Electronics, Measurements, Automation and Control Technology; Chapter 3: Signal and Data Processing, Data Mining, Applied and Computational Mathematics; Chapter 4: Information Technology Applications in Industry and Engineering.

Theorems and their proofs lie at the heart of mathematics. In speaking of the purely aesthetic qualities of theorems and proofs, G. H. Hardy wrote that in beautiful proofs 'there is a very high degree of unexpectedness, combined with inevitability and economy.' Charming Proofs present a collection of remarkable proofs in elementary mathematics that are exceptionally elegant, full of ingenuity, and succinct. By means of a surprising argument or a powerful visual representation, the proofs in this collection will invite readers to enjoy the beauty of mathematics, to share their discoveries with others, and to become involved in the process of creating new proofs. Charming Proofs is organized as follows. Following a short introduction about proofs and the process of creating proofs, the authors present, in twelve chapters, a wide and varied selection of proofs they consider charming. Topics include the integers, selected real numbers, points in the plane, triangles, squares and other polygons, curves, inequalities, plane tilings, origami, colorful proofs, threedimensional geometry, etc. At the end of each chapter are some challenges that will draw the reader into the process of...

Inequalities permeate mathematics, from the Elements of Euclid to operations research and financial mathematics. Yet too often the emphasis is on things equal to one another rather than unequal. While equalities and identities are without doubt important, they don't possess the richness and variety that one finds with inequalities. The objective of this book is to illustrate how use of visualization can be a powerful tool for better understanding some basic mathematical inequalities. Drawing pictures is a well-known method for problem solving, and we would like to convince you that the same is true when working with inequalities. We show how to produce figures in a systematic way for the illustration of inequalities; and open new avenues to creative ways of thinking and teaching. In addition, a geometric argument can not only show two things unequal, but also help the observer see just how unequal they are.

Certain geometric diagrams play a crucial role in visualizing mathematical proofs. Twenty of these icons of mathematics are presented in this book, where the authors explore the mathematics within them and the mathematics that can be created from them. A chapter is devoted to each icon, illustrating its presence in real life, its primary mathematical characteristics and how it plays a central role in visual proofs of a wide range of mathematical facts. Among these are classical results from plane geometry, properties of the integers, means and inequalities, trigonometric identities, theorems from calculus and puzzles from recreational mathematics. Each chapter concludes with a selection of challenges for the reader to explore further properties and applications of the icon. Those teaching undergraduate mathematics will find material here for problem solving sessions, as well as enrichment material for courses on proofs and mathematical reasoning.

A comprehensive framework for assessing strategies for managing risk and uncertainty, integrating theory and practice and synthesizing insights from many fields. This book offers a framework for making decisions under risk and uncertainty. Synthesizing research from economics, finance, decision theory, management, and other fields, the book provides a set of tools and a way of thinking that determines the relative merits of different strategies. It takes as its premise that we make better decisions if we use the whole toolkit of economics and related fields to inform our decision making. The text explores the distinction between risk and uncertainty and covers standard models of decision making under risk as well as more recent work on decision making under uncertainty, with a particular focus on strategic interaction. It also examines the implications of incomplete markets for managing under uncertainty. It presents four core strategies: a benchmark strategy (proceeding as if risk and uncertainty were low), a financial hedging strategy (valuable if there is much risk), an operational hedging strategy (valuable for conditions of much uncertainty), and a flexible strategy (valuable ...

Mathematical finance plays a vital role in many fields within finance and provides the theories and tools that have been widely used in all areas of finance. Knowledge of mathematics, probability, and statistics is essential to develop finance theories and test their validity through the analysis of empirical, real-world data. For example, mathematics, probability, and statistics could help to develop pricing models for financial assets such as equities, bonds, currencies, and derivative securities.

At present, computational methods have received considerable attention in economics and finance as an alternative to conventional analytical and numerical paradigms. This Special Issue brings together both theoretical and application-oriented contributions, with a focus on the use of computational techniques in finance and economics. Examined topics span on issues at the center of the literature debate, with an eye not only on technical and theoretical aspects but also very practical cases.