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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 anyonsis suggested as a modification of the Gibbs factor in the Bose and Fermistatistics. The proposed expressions are studied in the bosonic and fermioniclimits. The obtained virial coefficients coincide with those of free anyons upto the fourth and fifth virial coefficients (the proposed approach can beextended for higher ones as well) and up to the second order in the anyonicparameter. The effective excitation spectrum corresponding to anyons iscalculated.

Modeling free anyons at the bosonic and fermionic ends