Correlations in bivariate Pareto distributions

Abstract

Bivariate Pareto distributions have proven very useful in modelling lifetime data, hydrology, competing risk data, and many other datasets. In this paper, we explore Kendall tau and Gini correlations in the bivariate Pareto distributions, comparing with the popular Pearson correlation and robust quadrant correlation. It is interesting to establish the fact that zero of those correlations mutually imply independence in this family. We derive the variance of the asymptotic normality for each sample correlation via the influence function approach. When the second moment is finite, we demonstrate that the symmetric Gini correlation is asymptotically efficient as well as relatively efficient among finite samples. However, Kendall tau is more appealing in terms of compromising efficiency and robustness.

Keywords:

• Dependence
• correlations
• asymptotical efficiency
• influence function
• heavy-tailed
• robustness

Disclosure statement

No potential conflict of interest was reported by the author(s).