  We investigate the ground state of the one-dimensional interacting anyonic
system based on the exact Bethe ansatz solution for arbitrary coupling constant
($0\leq c\leq \infty$) and statistics parameter ($0\leq \kappa \leq \pi$). It
is shown that the density of state in quasi-momentum $k$ space and the ground
state energy are determined by the renormalized coupling constant $c'$. The
effect induced by the statistics parameter $\kappa$ exhibits in the momentum
distribution in two aspects: Besides the effect of renormalized coupling, the
anyonic statistics results in the nonsymmetric momentum distribution when the
statistics parameter $\kappa$ deviates from 0 (Bose statistics) and $\pi$
(Fermi statistics) for any coupling constant $c$. The momentum distribution
evolves from a Bose distribution to a Fermi one as $\kappa$ varies from 0 to
$\pi$. The asymmetric momentum distribution comes from the contribution of the
imaginary part of the non-diagonal element of reduced density matrix, which is
an odd function of $\kappa$. The peak at positive momentum will shift to
negative momentum if $\kappa$ is negative.
