Composite Method of Forming Approximating Distributions with an Arbitrary Phase Function

In this article we consider an approach to representation of distributions of probabili-ties in the form of the two-level composition of an integral kernel and a phase function which is generalization of the concept of density of random parameter distribution. Possibilities of giper-delta approximation of the phase function and its interrelation with the formation of phase-type distributions are shown. The method of approximating distributions formation on the basis of the arbitrary phase function by the method of derivatives is offered.