  A variational Monte Carlo calculation of the one-body density matrix and
momentum distribution of a system of Fermi hard rods (HR) is presented and
compared with the same quantities for its bosonic counterpart. The calculation
is exact within statistical errors since we sample the exact ground state wave
function, whose analytical expression is known. The numerical results are in
good agreement with known asymptotic expansions valid for Luttinger liquids. We
find that the difference between the absolute value of the bosonic and
fermionic density matrices becomes marginally small as the density increases.
In this same regime, the corresponding momentum distributions merge into a
common profile that is independent of the statistics. Non-analytical
contributions to the one--body density matrix are also discussed and found to
be less relevant with increasing density.
