Copula modeling dependence with continuous margins with application by using the package R

Abstract EN

This paper presents a class of multivariate probability models, known as “copula models”.

The aim of this paper is modeling dependence structure between random variables using copula.

The copula-based modeling of multivariate distributions with continuous margins is presented as a succession of rank-based tests: a multivariate test of randomness followed by a test of mutual independence and a series of goodness-of-fit tests.

All the tests under study are based on the empirical copula, which is a nonparametric rank-based estimator of the true unknown copula.

The principles of the tests are recalled and their implementation in the copula package R is briefly described.

Their use in the construction of a copula model from data is thoroughly illustrated on real financial and physical structure data.

The majority of the results thereby suggest that the Clayton copula and the t – copula provides an adequate representation of the empirical dependence structures for the performance analytics data and the urine analysis data, respectively.