Introduction to Copulas (eBook)

Roger B. Nelsen (Autor)

eBook Download: PDF

2007 | 2. Auflage
XIV, 276 Seiten
Springer New York (Verlag)
978-0-387-28678-5 (ISBN)

Infos

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.

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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 116 examples, 54 figures, and 167 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. The revised second edition includes new sections on extreme value copulas, tail dependence, and quasi-copulas.

Inhalt

Preface to the First Edition 7
Preface to the Second Edition 9
Contents 10
1 Introduction 13
2 Definitions and Basic Properties 18
2.1 Preliminaries 18
2.2 Copulas 21
2.3 Sklar’s Theorem 28
2.4 Copulas and Random Variables 35
2.5 The Fréchet-Hoeffding Bounds for Joint Distribution Functions 41
2.6 Survival Copulas 43
2.7 Symmetry 47
2.8 Order 49
2.9 Random Variate Generation 51
2.10 Multivariate Copulas 53
3 Methods of Constructing Copulas 61
3.1 The Inversion Method 61
3.2 Geometric Methods 69
3.3 Algebraic Methods 99
3.4 Copulas with Specified Properties 111
3.5 Constructing Multivariate Copulas 115
4 Archimedean Copulas 119
4.1 Definitions 119
4.2 One-parameter Families 124
4.3 Fundamental Properties 125
4.4 Order and Limiting Cases 145
4.5 Two- parameter Families 151
4.6 Multivariate Archimedean Copulas 161
5 Dependence 166
5.1 Concordance 166
5.2 Dependence Properties 195
5.3 Other Measures of Association 216
5.4 Tail Dependence 223
5.5 Median Regression 226
5.6 Empirical Copulas 228
5.7 Multivariate Dependence 231
6 Additional Topics 235
6.1 Distributions with Fixed Margins 235
6.2 Quasi-copulas 244
6.3 Operations on Distribution Functions 249
6.4 Markov Processes 252
References 258
List of Symbols 269
Index 271

Produkt-Details

• Erscheint lt. Verlag: 10.6.2007
• Reihe/Serie: Springer Series in Statistics
• Zusatzinfo: XIV, 272 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Themenwelt: Wirtschaft
• Schlagworte: Copula • Dependence • Mathematical Statistics • Measures of association • Multivariate distributions • parametric statistics • Quantitative Finance • Statistical Models • Statistics
• ISBN-10: 0-387-28678-0 / 0387286780
• ISBN-13: 978-0-387-28678-5 / 9780387286785