  We develop a bosonization approach to study the low temperature properties of
one-dimensional gas of particles obeying fractional exclusion statistics (FES).
It is shown that such ideal gas reproduces the low-energy excitations and
asymptotic exponents of a one-component Luttinger liquid (with no internal
degrees of freedom). The bosonized effective theory at low energy (or
temperature) is identified to a $c=1$ conformal field theory (CFT) with
compactified radius determined by the statistics parameter $\lambda$. Moreover,
this CFT can be put into a form of the harmonic fluid description for Luttinger
liquids, with the Haldane controlling parameter identified with the statistics
parameter (of quasi-particle excitations). Thus we propose to use the latter to
characterize the fixed points of 1-d Luttinger liquids. Such a characterization
is further shown to be valid for generalized ideal gas of particles with mutual
statistics in momentum space and for non-ideal gas with Luttinger-type
interactions: In either case, the low temperature behavior is controlled by an
effective statistics varying in a fixed-point line.
