  In the framework of Gibbs statistical theory, the issue of the distribution
of particle sizes forming the statistical system and the moments of this
distribution are considered. This task is relevant for a wide variety of
applications. The distribution for particle sizes and moments of this quantity
are determined from probabilistic considerations. Particle size depends on
interactions in the system, on the compressibility factor, on the number of
interacting particles, on the volume of the system. The expressions for the
intrinsic volume of particles are substituted into the equations of state
written using the theory of excluded volume for various expressions of the
exclusion factor. The equations of state thus obtained can be considered as a
refinement of the equation of state, a transition to a higher level of
description.
