Nelsen An Introduction to Copulas

2. Auflage 2006
ISBN: 978-0-387-28678-5
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 276 Seiten

Reihe: Springer Series in Statistics

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. This book is suitable as a text or for self-study.

Autoren/Hrsg.

Nelsen, Roger B.

Inhaltsverzeichnis

1;Preface to the First Edition;7
2;Preface to the Second Edition;9
3;Contents;10
4;1 Introduction;13
5;2 Definitions and Basic Properties;18
5.1;2.1 Preliminaries;18
5.2;2.2 Copulas;21
5.3;2.3 Sklar’s Theorem;28
5.4;2.4 Copulas and Random Variables;35
5.5;2.5 The Fréchet-Hoeffding Bounds for Joint Distribution Functions;41
5.6;2.6 Survival Copulas;43
5.7;2.7 Symmetry;47
5.8;2.8 Order;49
5.9;2.9 Random Variate Generation;51
5.10;2.10 Multivariate Copulas;53
6;3 Methods of Constructing Copulas;61
6.1;3.1 The Inversion Method;61
6.2;3.2 Geometric Methods;69
6.3;3.3 Algebraic Methods;99
6.4;3.4 Copulas with Specified Properties;111
6.5;3.5 Constructing Multivariate Copulas;115
7;4 Archimedean Copulas;119
7.1;4.1 Definitions;119
7.2;4.2 One-parameter Families;124
7.3;4.3 Fundamental Properties;125
7.4;4.4 Order and Limiting Cases;145
7.5;4.5 Two- parameter Families;151
7.6;4.6 Multivariate Archimedean Copulas;161
8;5 Dependence;166
8.1;5.1 Concordance;166
8.2;5.2 Dependence Properties;195
8.3;5.3 Other Measures of Association;216
8.4;5.4 Tail Dependence;223
8.5;5.5 Median Regression;226
8.6;5.6 Empirical Copulas;228
8.7;5.7 Multivariate Dependence;231
9;6 Additional Topics;235
9.1;6.1 Distributions with Fixed Margins;235
9.2;6.2 Quasi-copulas;244
9.3;6.3 Operations on Distribution Functions;249
9.4;6.4 Markov Processes;252
10;References;258
11;List of Symbols;269
12;Index;271