  We show that it is possible to replace the actual implicit distribution
function of the fractional exclusion statistics by an explicit one whose form
does not change with the parameter $\alpha$. This alternative simpler
distribution function given by a generalization of Pauli exclusion principle
from the level of the maximal occupation number is not completely equivalent to
the distributions obtained from the level of state number counting of the
fractional exclusion particles. Our result shows that the two distributions are
equivalent for weakly bosonized fermions ($\alpha>>0$) at not very high
temperatures.
