In this paper, we propose a new method to construct the joint probability model from a specified first-order distribution and correlation structure. The construction procedure can be interpreted in two ways: (1) It embodies the maximum entropy principle, or (2) It is considered as a correlated non-Gaussian source generated by a nonlinear transformation from a correlated Gaussian source. Its stochastic properties [mean,correlation] and information-theoretic properties [entropy, rate-distortion bound] are examined. An example for the lognormal distribution is given to illustrate the construction process and the characteristics of the source. This approach should remove the limitations imposed by earlier methods, and make for more realistic modeling of medical images.