An Introduction to CopulasCopulas 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. |
Contents
| 1 | |
Methods of Constructing Copulas ______________________________________ _ 51 | 50 |
Archimedean Copulas _________________________________________________ __109 | 109 |
Dependence _____________________________________________________________ | 157 |
Additional Topics ______________________________________________________ __227 | 226 |
| 262 | |
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2-increasing absolutely continuous Ali-Mikhail-Haq family Alsina analogous Archimedean copulas bivariate distribution C1 and C2 Chapman-Kolmogorov equations chimedean completely monotonic construct continuous random variables convex Corollary cubic sections defined Definition denote dependence properties diagonal section distribution func equivalent Example Exercise exponential distribution F and G family of Archimedean family of copulas following theorem Fréchet function H Genest graph hence inequality joint distribution function Kendall’s tau Lemma Let C9 line segments marginal distribution margins F Markov process Marshall-Olkin measures of association monotone function multivariate n-copula n-dimensional Nelsen nondecreasing nonincreasing Note ordinal sum P[X S pair parameter population version proof quadrant dependence quasi-copula rectangle respectively satisfies Scatterplots Sect Show shuffle Sklar’s theorem Spearman’s rho Statist stochastic strictly increasing subcopula subset survival copula survival function symmetric tail monotonicity tion function uniform 0,1 variables whose joint variables with joint X and Y yields