Local dependence in bivariate copulae with Beta marginals

Abstract

The local dependence function (LDF) describes changes in the correlation structure of continuous bivariate random variables along their range. Bivariate density functions with Beta marginals can be used to model jointly a wide variety of data with bounded outcomes in the (0,1) range, e.g. proportions. In this paper we obtain expressions for the LDF of bivariate densities constructed using three different copula models (Frank, Gumbel and Joe) with Beta marginal distributions, present examples for each, and discuss an application of these models to analyse data collected in a study of marks obtained on a statistics exam by postgraduate students.

Keywords

• beta distribution
• local dependence function
• copula
• bivariate densities