Coauthors: Davide Meneguzzo

The Latin word "copula" denotes linking or connecting between parts. This word has been adopted in statistics to denote a class of functions allowing to build crossdependent multivariate distributions. Although the terms "correlation" and "dependence" are often used interchangeably, the former is a rather particular kind of dependence measure between random variables. As such, it suffers from inconveniences due to its limitation in capturing other forms of dependence. For instance, it is not difficult to find examples of dependent variables displaying zero correlation. The problem of modeling dependence structures is that this feature does not always show out of the joint distribution function under consideration. It would be of some help to separate the statistical properties of each variable from their dependence structure. Copula functions provide us with a viable way to achieve this goal. This chapter is organized as follows. Section 8.1 introduces the notion of copula and related definitions. Section 8.2 presents an overview of major concepts of dependence and examines their link to copulas. Sections 8.3 and 8.4 exhibit the most important families of copulas together with their properties. Section 8.5 is devoted to the statistical inference of copula functions. Section 8.6 discusses Monte Carlo simulation techniques. Section 8.7 concludes with a few remarks and comments.

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Comments

Page 244: the line of code

norminv(ul(i))^2 + norminv(u2(j))*2

must be replaced by

norminv(ul(i))^2 + norminv(u2(j))^2