Local and Interval Dependence for Bivariate Gamma distribution Created by Archimedean Copula

Abstract

The Interval Dependence Structure (IDS) and Local Dependence Function (LDF) are tools used to measure possible changes that occur in the correlation of bivariate random variables at each point acrossthe whole domain. Bivariate distribution functionswith Gamma marginals are used to construct correlated models that joint a widespread variety of data having positive values. In this paper, to deriveformulas to measure the LDF and IDS, bivariate Gamma distribution are constructedfor two different copula models (Frank, Clyton). Additionally, the key assumptions and properties for each model are explained and then the two approaches are compared based on the observed differences between the two measures, IDS and, LDF using an example from each model.