Bivariate dependence measures and bivariate competing risks models under the generalized FGM copula

Abstract

The first part of this paper reviews the properties of bivariate dependence measures (Spearman’s rho, Kendall’s tau, Kochar and Gupta’s dependence measure, and Blest’s coefficient) under the generalized Farlie–Gumbel–Morgenstern (FGM) copula. We give a few remarks on the relationship among the bivariate dependence measures, derive Blest’s coefficient, and suggest simplifying the previously obtained expression of Kochar and Gupta’s dependence measure. The second part of this paper derives some useful measures for analyzing bivariate competing risks models under the generalized FGM copula. We obtain the expression of sub-distribution functions under the generalized FGM copula, which has not been discussed in the literature. With the Burr III margins, we show that our expression has a closed form and generalizes the reliability measure previously obtained by Domma and Giordano (Stat Pap 54(3):807–826, 2013).