# An Introduction to Copulas

Springer Science & Business Media, Jan 13, 2006 - Business & Economics - 269 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 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.

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### 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

### 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.