The Pareto Copula, aggregation of risks and the Emperor's socks

The copula of a multivariate distribution is the distribution transformed so that one dimensional marginal distributions are uniform. We review a different transformation of a multivariate distribution which yields standard Pareto for the marginal distributions and the resulting distribution we call the Pareto copula. Use of the Pareto copula has a certain claim to naturalness when considering asymptotic limit distributions for sums, maxima and empirical processes. We discuss implications for aggregation of risk and offer some examples.     «

The copula of a multivariate distribution is the distribution transformed so that one dimensional marginal distributions are uniform. We review a different transformation of a multivariate distribution which yields standard Pareto for the marginal distributions and the resulting distribution we call the Pareto copula. Use of the Pareto copula has a certain claim to naturalness when considering asymptotic limit distributions for sums, maxima and empirical processes. We discuss implications for...     »