Chp 1 Introduction

What are copulas? From one point of view, copulas are functions that join or “couple”" multivariate distribution functions to their one-dimensional marginal distribution functions. Alternatively, copulas are multivariate distribution functions whose one-dimensional margins are uniform on the interval (0,1)

1940s Wassily Hoeffding
1951 Fréchet bounds and Fréchet classes
1959 Abe Sklar, first use of term “copula”
1958-1976 probabilistic metric spaces –> Archimedean copulas
1981 Schweizer and Wolff copulas and dependence

This book concentrates on the construction of families of multivariate distributions ans the study of dependence