Copulas: As a Measure of Dependence

The study of the relationship between two or more random variables remains an important problem in Statistical Science. Copulas provide a convenient way to express joint distributions of two or more random vari- ables. With a copula we can separate the joint distribution into two contributions: the marginal distributions of each variable by itself, and the copula that combines these into a joint distribution. One basic result is that any joint distribution can be expressed in this man- ner. Another convenience is that the conditional distributions can be readily ex-pressed using the copula. Copulas are a useful tool for understanding relationships among multivariate variables, and are important tools for describing the dependence structure between random variables, with different copulas representing different dependencies. Since the study of dependence is critically important in Statistics in order to carry out reliable analyses, understanding and applying results from copulas can be very beneficial. The main ob- ject of this paper is that the advantages of using a copula over correlation were to model dependencies between two or more variables.