FF-Type Multivariate Models in an Enforced Regression Paradigm

We consider the stochastic dependence of a given random variable Y on a set of its explanatory variables. Using our earlier method of parameter dependence we obtain a description of this dependence in the form of a conditional probability distribution of Y, given any realization of the explanatory variables. We obtain a wide class of conditional distributions, including most of the important non-Gaussian cases, in an explicit, tractable, analytical form which, basically, is not known in the current literature. This fact automatically prompts one to extend the existing regression models, which usually are given in form of conditional expectations, to models based on the corresponding conditional probability distributions, given the same values of the data. The latter models, obviously, contain more statistical information and thus are expected to give better predictions. We also included some, related to the conditional, multivariate probability densities.