Parametric dominance relations for distributions obtained by composition

The so called T-X family provides an interesting new method for generating distributions by composing (possibly parametric) distribution and quantile functions. Such an approach makes it possible to add parameters to an existing model, in order to obtain a new and more flexible one. In this framework, we study the conditions under which distributions obtained through the T-X method can be ranked by a dominance relation, such as the stochastic dominance of first and second degree.