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

翻译：针对一对相依随机寿命，其相依性由时间变换指数模型描述，本文给出了它们和的分布的解析表达式。这些表达式通过使用多元失真表示的联合分布获得，该表示是经典copula表示的一种替代方法。由于该方法能以简单形式获得条件分布及其逆函数，因此还展示了如何利用分位数回归技术，根据其中一个变量的值（或反之）预测和的值。