  The violation of the Pauli principle has been surmised in several models of
the Fractional Exclusion Statistics and successfully applied to several quantum
systems. In this paper, a classical alternative of the exclusion statistics is
studied using the maximum entropy methods. The difference between the
Bose-Einstein statistics and the Maxwell-Boltzmann statistics is understood in
terms of a separable quantity, namely the degree of indistinguishability.
Starting from the usual Maxwell-Boltzmann microstate counting formula, a
special restriction related to the degree of indistinguishability is
incorporated using Lagrange multipliers to derive the probability distribution
function at equilibrium under NVE conditions. It is found that the resulting
probability distribution function generates real positive values within the
permissible range of parameters. For a dilute system, the probability
distribution function is intermediate between the Fermi-Dirac and Bose-Einstein
statistics and follows the exclusion principle. Properties of various variables
of this novel statistical model are studied and possible application to
classical thermodynamics is discussed.
