  We characterize a comprehensive family of $d$-variate exogenous shock models.
Analytically, we consider a family of multivariate distribution functions that
arises from ordering, idiosyncratically distorting, and finally multiplying the
arguments. Necessary and sufficient conditions on the involved distortions to
yield a multivariate distribution function are given. Probabilistically, the
attainable set of distribution functions corresponds to a large class of
exchangeable exogenous shock models. Besides, the vector of exceedance times of
an increasing additive stochastic process across independent exponential
trigger variables is shown to constitute an interesting subclass of the
considered distributions and yields a second probabilistic model. The
alternative construction is illustrated in terms of two examples.
