An Introduction to Copulas
Title | An Introduction to Copulas PDF eBook |
Author | Roger B. Nelsen |
Publisher | Springer Science & Business Media |
Pages | 227 |
Release | 2013-03-09 |
Genre | Mathematics |
ISBN | 1475730764 |
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.
An Introduction to Copulas
Title | An Introduction to Copulas PDF eBook |
Author | Roger B. Nelsen |
Publisher | Springer Science & Business Media |
Pages | 276 |
Release | 2007-06-10 |
Genre | Mathematics |
ISBN | 0387286780 |
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. This book is suitable as a text or for self-study.
Elements of Copula Modeling with R
Title | Elements of Copula Modeling with R PDF eBook |
Author | Marius Hofert |
Publisher | Springer |
Pages | 274 |
Release | 2019-01-09 |
Genre | Business & Economics |
ISBN | 3319896350 |
This book introduces the main theoretical findings related to copulas and shows how statistical modeling of multivariate continuous distributions using copulas can be carried out in the R statistical environment with the package copula (among others). Copulas are multivariate distribution functions with standard uniform univariate margins. They are increasingly applied to modeling dependence among random variables in fields such as risk management, actuarial science, insurance, finance, engineering, hydrology, climatology, and meteorology, to name a few. In the spirit of the Use R! series, each chapter combines key theoretical definitions or results with illustrations in R. Aimed at statisticians, actuaries, risk managers, engineers and environmental scientists wanting to learn about the theory and practice of copula modeling using R without an overwhelming amount of mathematics, the book can also be used for teaching a course on copula modeling.
Analyzing Dependent Data with Vine Copulas
Title | Analyzing Dependent Data with Vine Copulas PDF eBook |
Author | Claudia Czado |
Publisher | |
Pages | |
Release | 2019 |
Genre | Copulas (Mathematical statistics) |
ISBN | 9783030137861 |
This textbook provides a step-by-step introduction to the class of vine copulas, their statistical inference and applications. It focuses on statistical estimation and selection methods for vine copulas in data applications. These flexible copula models can successfully accommodate any form of tail dependence and are vital to many applications in finance, insurance, hydrology, marketing, engineering, chemistry, aviation, climatology and health. The book explains the pair-copula construction principles underlying these statistical models and discusses how to perform model selection and inference. It also derives simulation algorithms and presents real-world examples to illustrate the methodological concepts. The book includes numerous exercises that facilitate and deepen readers understanding, and demonstrates how the R package VineCopula can be used to explore and build statistical dependence models from scratch. In closing, the book provides insights into recent developments and open research questions in vine copula based modeling. The book is intended for students as well as statisticians, data analysts and any other quantitatively oriented researchers who are new to the field of vine copulas. Accordingly, it provides the necessary background in multivariate statistics and copula theory for exploratory data tools, so that readers only need a basic grasp of statistics and probability.
Principles of Copula Theory
Title | Principles of Copula Theory PDF eBook |
Author | Fabrizio Durante |
Publisher | CRC Press |
Pages | 331 |
Release | 2015-07-01 |
Genre | Mathematics |
ISBN | 1439884447 |
This book gives readers the solid and formal mathematical background to apply copulas to a range of mathematical areas, such as probability, real analysis, measure theory, and algebraic structures. The authors prove the results as simply as possible and unify various methods scattered throughout the literature in common frameworks, including shuffles of copulas. They also explore connections with related functions, such as quasi-copulas, semi-copulas, and triangular norms, that have been used in different domains.
Copulas
Title | Copulas PDF eBook |
Author | Regina Pustet |
Publisher | OUP Oxford |
Pages | 282 |
Release | 2003-06-12 |
Genre | Language Arts & Disciplines |
ISBN | 0191555304 |
Copulas (in English, the verb to be) are conventionally defined functionally as a means of relating elements of clause structure, especially subject and complement, and considered to be semantically empty or meaningless.They have received relatively little attention from linguists. Dr Pustet in this extensive cross-linguistic study goes some way towards correcting this neglect. In doing so she takes issue with both accepted definition and description. She presents an analysis of grammatical descriptions of over 160 languages drawn from the language families of the world. She shows that some languages have a single copula, others several, and some none at all. In a series of statistical analyses she seeks to explain why by linking the distribution of copulas to variations in lexical categorization and syntactic structure. She concludes by advancing a comprehensive theory of copularization which she relates to language classification and to theories of language change, notably grammaticalization.
Copula Theory and Its Applications
Title | Copula Theory and Its Applications PDF eBook |
Author | Piotr Jaworski |
Publisher | Springer Science & Business Media |
Pages | 338 |
Release | 2010-07-16 |
Genre | Mathematics |
ISBN | 3642124658 |
Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 50's, copulas have gained considerable popularity in several fields of applied mathematics, such as finance, insurance and reliability theory. Today, they represent a well-recognized tool for market and credit models, aggregation of risks, portfolio selection, etc. This book is divided into two main parts: Part I - "Surveys" contains 11 chapters that provide an up-to-date account of essential aspects of copula models. Part II - "Contributions" collects the extended versions of 6 talks selected from papers presented at the workshop in Warsaw.