An Introduction to Copulas

Front Cover
Springer Science & Business Media, Jan 13, 2006 - Business & Economics - 269 pages
2 Reviews

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.

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 and Proofs Without Words II: More Exercises in Visual Thinking, published by the Mathematical Association of America.

  

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

V
10
Definitions and Basic Properties
14
22 Copulas
17
23 Sklars Theorem
24
VI
28
VII
30
VIII
32
IX
34
XXXI
135
XXXII
141
XXXIV
146
XXXV
150
XXXVI
151
XXXVII
155
XXXVIII
156
XL
158

X
36
XI
38
26 Survival Copulas
39
XII
40
XIII
42
210 Multivariate Copulas
49
XIV
51
XVI
52
XVII
55
Exercises
57
Methods of Constructing Copulas
59
312 The Circular Uniform Distribution
63
XVIII
64
32 Geometric Methods
67
Exercises
72
XIX
74
XX
76
325 Copulas with Prescribed Horizontal or Vertical Sections
84
XXI
86
XXII
89
326 Copulas with Prescribed Diagonal Sections
92
Exercises
94
33 Algebraic Methods
97
XXIV
99
XXV
101
333 A Copula Transformation Method
102
334 Extreme Value Copulas
105
34 Copulas with Specified Properties
109
XXVIII
114
XXIX
115
XXX
132
XLI
165
511 Kendalls tau
167
XLII
171
Exercises
174
Exercises
180
XLIII
185
XLIV
186
514 Other Concordance Measures
189
XLV
191
52 Dependence Properties
195
523 Stochastic Monotonicity Corner Set Monotonicity and Likelihood Ratio Dependence
204
XLVI
207
XLVIII
211
Exercises
213
XLIX
214
53 Other Measures of Association
216
L
217
LI
219
Exercises
222
55 Median Regression
227
LII
233
LIII
236
LIV
240
LV
241
LVI
244
LVII
248
Exercises
250
References
263
LVIII
265
Copyright

Common terms and phrases

Popular passages

Page 256 - JACKSON . A User's Guide to Principle Components JOHN . Statistical Methods in Engineering and Quality Assurance JOHNSON . Multivariate Statistical Simulation JOHNSON and BALAKRISHNAN . Advances in the Theory and Practice of Statistics: A Volume in Honor of Samuel Kotz JUDGE, GRIFFITHS, HILL.
Page 3 - For any * ^ 0, the value d(p, q) at x can be interpreted as "the probability that the distance between p and q is less than x"; it was approach of K.
Page 267 - Sklar, A. (1974) Operations on distribution functions not derivable from operations on random variables, Studia Math. 52, 43-52.
Page 4 - In their words, since ... under almost surely increasing transformations of (the random variables), the copula is invariant while the margins may be changed at will, it follows that it is precisely the copula which captures those properties of the joint distribution which are invariant under almost surely strictly increasing transformations.

References to this book

All Book Search results »

About the author (2006)

Roger B. Nelsen (BA DePauw University, Ph.D. Duke University) is Professor Emeritus of Mathematics at Lewis and Clark College. Roger has been an AP Calculus Reader for many years and has authored or co-authored four books for the MAA: Proofs Without Words: Exercises in Visual Thinking (1993); Proofs Without Words II: More Exercises in Visual Thinking (2000); Math Made Visual: Creating Images for Understanding Mathematics (with Claudi Alsina, 2006); and When Less Is More: Visualizing Basic Inequalities (with Claudi Alsina, 2009).