  In the paper, two-parametric models of fractional statistics are proposed in
order to determine the functional form of the distribution function of free
anyons. From the expressions of the second and third virial coefficients, an
approximate correspondence is shown to hold for three models, namely, the
nonextensive Polychronakos statistics and both the incomplete and the
nonextensive modifications of the Haldane--Wu statistics. The difference occurs
only in the fourth virial coefficient leading to a small correction in the
equation of state. For the two generalizations of the Haldane--Wu statistics,
the solutions for the statistics parameters $g,q$ exist in the whole domain of
the anyonic parameter $\alpha\in[0;1]$, unlike the nonextensive Polychronakos
statistics. It is suggested that the search for the expression of the anyonic
distribution function should be made within some modifications of the
Haldane--Wu statistics.
