Modeling Multivariate Distributions with Continuous Margins Using thecopulaRPackage

Abstract

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 consideration 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 R package is briefly described. Their use in the construction of a copula model from data is thoroughly illustrated on real insurance and financial data.

Upper tail dependence in rainfall extremes: would we know it if we saw it?

“…The authors wish to thank Prof. Zhengjun Zhang (University of Wisconsin, US) for his advice about the quotient correlation test, and Prof. Qiang Zhang (Sun Yat-sen University, China) and three anonymous reviewers for their remarks and criticisms that helped improve the quality of the original manuscript. The analyses were performed in R (R Core Team 2013) by using the contributed packages POT (Ribatet 2006), mvtnorm (Genz and Bretz 2009;Genz et al 2011), and copula (Yan 2007;Kojadinovic and Yan 2010). The authors and maintainers of this software are gratefully acknowledged.…”

Ornstein - Uhlenbeck type processes with heavy distribution tails

“…We can see that, in both cases, there is a reasonable agreement of the empirical data with the fitted Gauss copulas. To confirm this observation numerically, we used a recently suggested method for calculating approximate P -values for testing the goodness-of-fit by parametric copula families [11], [12]. As the method is valid for i.i.d.…”

Numerical analysis of the accuracy of bivariate quantile distributions utilizing copulas compared to the GUM supplement 2 for oil pressure balance uncertainties

“…; u n T directly with custom written computer code through various parameter optimization approaches for a range of copula families of which Table 4 is only a small selection of the very extensive range of possible copula families this is no longer strictly essential. This is due to the fact that Yan [36] developed a R based package copula which is now readily available to researchers worldwide, and which has subsequently been expanded by Kojadinovic and Yan [37] for multivariate distribution modelling using copulas. As a result the use of R based open source statistical software from the Comprehensive R Archive Network is now commonly available to researchers worldwide and is accepted as a standard statistical tool within the statistics community.…”