  We investigate the ground-state properties of anyons confined in
one-dimensional optical lattices with a weak harmonic trap using the exact
numerical method based on Jordan-Wigner transformation. It is shown that in the
Bose limit ($\chi =1$) and Fermi limit ($\chi=0$) the momentum distributions
are symmetric but in between they are asymmetric. It turns out that the origin
of asymmetry comes from the fractional statistics that anyons obey. The
occupation distribution and the modulus of natural orbitals show crossover
behaviours from the Bose limit to the Fermi limit.
