An Introduction to Copulas

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

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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

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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.

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