Marginals vs. covariance in joint distribution theory

Cohen (1966, 1995) has proposed a method for constructing joint distributions of arbitrary physical quantities, in direct generalization of joint time-frequency representations. We investigate the covariance properties of this procedure and caution that in its present form it cannot generate all possible distributions. Using group theory, we extend Cohen´s construction to a more general form that can be customized to satisfy specific marginal and covariance requirements