Composition operator for densities of continuous variables

The paper presents an operator of composition for densities of continuous random variables and analyzes its properties, particularly the assertions useful for marginalization, lemmata concerning the conditional independence, theorems describing entropy of the composition and assertions for reordering of composed densities in the model. The generalized function of Dirac delta is proposed as a degenerated distribution allowing the expression of operation of conditioning using the composition of Dirac delta with a continuous density or with a compositional model. A special case of composition within the exponential family of distributions is considered.