# An Introduction to Copulas

Springer Science & Business Media, 1999 - Business & Economics - 216 pages
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.

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### Contents

 Introduction 1 Definitions and Basic Properties 5 22 Copulas 8 23 Sklars Theorem 14 24 Copulas and Random Variables 21 25 The FréchetHoeffding Bounds for Joint Distribution Functions of Random Variables 26 26 Survival Copulas 28 27 Symmetry 31
 44 Order and Limiting Cases 108 45 Twoparameter Families 114 46 Multivariate Archimedean Copulas 121 Dependence 125 52 Dependence Properties 151 53 Other Measures of Association 169 54 Median Regression 175 55 Empirical Copulas 176

 28 Order 34 29 Random Variate Generation 35 210 Multivariate Copulas 37 Methods of Constructing Copulas 45 32 Geometric Methods 52 33 Algebraic Methods 79 34 Constructing Multivariate Copulas 84 Archimedean Copulas 89 42 Oneparameter Families 93
 56 Multivariate Dependence 179 Additional Topics 183 62 Operations on Distribution Functions 191 63 Markov Processes 194 References 201 List of Symbols 211 Index 213 Copyright

### Popular passages

Page 201 - Distribution free tests of independence based on the sample distribution function.
Page 202 - DALL'AGLIO, G. Les fonctions extremes de la classe de Frechet a 3 dimensions.

### About the author (1999)

Roger B. Nelsen received his B.A. in mathematics from DePauw University in 1964 and his Ph.D. in mathematics from Duke University in 1969. Roger was elected to Phi Beta Kappa and Sigma Xi. His previous books include Proofs Without Words: Exercises in Visual Thinking, MAA 1993; An Introduction to Copulas, Springer, 1999 (2nd edition 2006); Proofs Without Words II: More Exercises in Visual Thinking, MAA, 2000; and Math Made Visual: Creating Images for Understanding Mathematics (with Claudi Alsina), MAA, 2006.