【书名】 An Introduction to Copulas
【作者】Nelsen, Roger B.
【出版社】Springer
【版本】2nd ed.
【出版日期】2006
【文件格式】PDF
【文件大小】2.28 MB
【页数】250 Pages
【ISBN出版号】ISBN: 978-0-387-28659-4
【资料类别】计量经济学，统计学
【市面定价】59.96 Dollars Amazon Hardcover
【扫描版还是影印版】影印版
【是否缺页】完整
【关键词】Copulas
【内容简介】
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.
【目录】
1 Introduction 1
2 Definitions and Basic Properties 7
2.1 Preliminaries 7
2.2 Copulas 10
Exercises 2.1-2.11 14
2.3 Sklar’s Theorem 17
2.4 Copulas and Random Variables 24
Exercises 2.12-2.17 28
2.5 The Fréchet-Hoeffding Bounds for Joint Distribution
Functions of Random Variables 30
2.6 Survival Copulas 32
Exercises 2.18-2.26 34
2.7 Symmetry 36
2.8 Order 38
Exercises 2.27-2.33 39
2.9 Random Variate Generation 40
2.10 Multivariate Copulas 42
Exercises 2.34-2.37 48
3 Methods of Constructing Copulas 51
3.1 The Inversion Method 51
3.1.1 The Marshall-Olkin Bivariate Exponential Distribution 52
3.1.2 The Circular Uniform Distribution 55
Exercises 3.1-3.6 57
3.2 Geometric Methods 59
3.2.1 Singular Copulas with Prescribed Support 59
3.2.2 Ordinal Sums 63
Exercises 3.7-3.13 64
3.2.3 Shuffles of M 67
3.2.4 Convex Sums 72
Exercises 3.14-3.20 74
3.2.5 Copulas with Prescribed Horizontal or Vertical Sections 76
3.2.6 Copulas with Prescribed Diagonal Sections 84
Exercises 3.21-3.34 86
3.3 Algebraic Methods 89
3.3.1 Plackett Distributions 89
3.3.2 Ali-Mikhail-Haq Distributions 92
3.3.3 A Copula Transformation Method 94
3.3.4 Extreme Value Copulas 97
Exercises 3.35-3.42 99
3.4 Copulas with Specified Properties 101
3.4.1 Harmonic Copulas 101
3.4.2 Homogeneous Copulas 101
3.4.3 Concave and Convex Copulas 102
3.5 Constructing Multivariate Copulas 105
4 Archimedean Copulas 109
4.1 Definitions 109
4.2 One-parameter Families 114
4.3 Fundamental Properties 115
Exercises 4.1-4.17 132
4.4 Order and Limiting Cases 135
4.5 Two-parameter Families 141
4.5.1 Families of Generators 141
4.5.2 Rational Archimedean Copulas 146
Exercises 4.18-4.23 150
4.6 Multivariate Archimedean Copulas 151
Exercises 4.24-4.25 155
5 Dependence 157
5.1 Concordance 157
5.1.1 Kendall’s tau 158
Exercises 5.1-5.5 165
5.1.2 Spearman’s rho 167
Exercises 5.6-5.15 171
5.1.3 The Relationship between Kendall’s tau
and Spearman’s rho 174
5.1.4 Other Concordance Measures 180
Exercises 5.16-5.21 185
5.2 Dependence Properties 186
5.2.1 Quadrant Dependence 187
Exercises 5.22-5.29 189
5.2.2 Tail Monotonicity 191
5.2.3 Stochastic Monotonicity, Corner Set Monotonicity,
and Likelihood Ratio Dependence 195
Exercises 5.30-5.39 204
5.3 Other Measures of Association 207
5.3.1 Measures of Dependence 207
5.3.2 Measures Based on Gini’s Coefficient 211
Exercises 5.40-5.46 213
5.4 Tail Dependence 214
Exercises 5.47-5.50 216
5.5 Median Regression 217
5.6 Empirical Copulas 219
5.7 Multivariate Dependence 222
6 Additional Topics 227
6.1 Distributions with Fixed Margins 227
Exercises 6.1-6.5 233
6.2 Quasi-copulas 236
Exercises 6.6-6.8 240
6.3 Operations on Distribution Functions 241
6.4 Markov Processes 244
Exercises 6.9-6.13 248
References 251
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