On sums of dependent random lifetimes under the time-transformed exponential model

Abstract For a given pair of random lifetimes whose dependence is described by time-transformed exponential model, we provide analytical expressions for the distribution their sum. These are obtained using representation joint in terms bivariate distortions, which an alternative approach to classical copula representation. Since this allows one obtain conditional distributions and inverses simple form, then it also shown how can be used predict value sum from variables (or vice versa) quantile regression techniques.