  The univariate distorted distribution were introduced in risk theory to
represent changes (distortions) in the expected distributions of some risks.
Later they were also applied to represent distributions of order statistics,
coherent systems, proportional hazard rate (PHR) and proportional reversed
hazard rate (PRHR) models, etc. In this paper we extend this concept to the
multivariate setup. We show that, in some cases, they are a valid alternative
to the copula representations especially when the marginal distributions may
not be easily handled. Several relevant examples illustrate the applications of
such representations in statistical modeling. They include the study of paired
(dependent) ordered data, joint residual lifetimes, order statistics and
coherent systems.
