Joint modelling of the body and tail of bivariate data

In situations where both extreme and non-extreme data are of interest, modelling the whole data set accurately is important. In a univariate framework, modelling the bulk and tail of a distribution has been studied before, but little work has been done when more than one variable is of concern. We propose a dependence model that blends two copulas with different characteristics over the whole range of the data support. One copula is tailored to the bulk and the other to the tail, with a dynamic weighting function employed to transition smoothly between them. We investigate tail dependence properties numerically and use simulation to confirm that the blended model is flexible enough to capture a wide variety of structures. We apply our model to study the dependence between temperature and ozone concentration at two sites in the UK and compare with a single copula fit. The proposed model provides a better, more flexible, fit to the data, and is also capable of capturing complex dependence structures.