The Stingray Copula for Negative Dependence

We present a new single-parameter bivariate copula, called the Stingray, that is dedicated to representing negative dependence, and it nests the Independence copula. The Stingray copula is generated in a relatively novel way; it has a simple form and is always defined over the full support, unlike many copulas that model negative dependence. We provide visualizations of the copula, derive several dependence properties, and compute basic concordance measures. We compare it with other copulas and joint distributions with respect to the extent of dependence it can capture, and we find that the Stingray copula outperforms most of them while remaining competitive with well-known, widely used copulas such as the Gaussian and Frank copulas. Moreover, we show, through simulation, that the dependence structure it represents cannot be fully captured by these copulas, as it is asymmetric. We also show how the non-parametric Spearman’s rho measure of concordance can be used to formally test the hypothesis of statistical independence. As an illustration, we apply it to a financial data sample from the building construction sector in order to model the negative relationship between the level of capital employed and its gross rate of return.