  The topology of two-dimensional movement allows for existing of anyons --
particles obeying statistics intermediate between that of bosons and fermions.
In this article, the functional form of the occupation numbers of free anyons
is suggested as a modification of the Gibbs factor in the Bose and Fermi
statistics. The proposed expressions are studied in the bosonic and fermionic
limits. The obtained virial coefficients coincide with those of free anyons up
to the fourth and fifth virial coefficients (the proposed approach can be
extended for higher ones as well) and up to the second order in the anyonic
parameter. The effective excitation spectrum corresponding to anyons is
calculated.
