Validation of positive quadrant dependence

- We provide a reparametrization of positive quadrant dependence.
- We propose a visualization of dependence structure of data and copula models.
- We introduce two tests for positive quadrant dependence.
- We find interesting properties of finite sample distribution of empirical copula.

Quadrant dependence is a useful dependence notion of two random variables, widely applied in reliability, insurance and actuarial sciences. The interest in this dependence structure ranges from modeling it, throughout measuring its strength and investigations on how increasing the dependence effects of several reliability and economic indexes, to hypothesis testing on the dependence. In this paper, we focus on testing for positive quadrant dependence. We propose two new tests for verifying positive quadrant dependence. We prove novel results on finite sample behavior of power function of one of the proposed tests as well as evaluate and compare the two new solutions with the best existing ones, via a simulation study. These comparisons demonstrate that the new solutions are slightly weaker in detecting positive quadrant dependence modeled by classical bivariate models and outperform the best existing solutions when some mixtures, regression and heavy-tailed models have to be detected. Finally, the methods introduced in the paper are applied to real life insurance data, to assess the dependence and test them for positive quadrant dependence.