  A set of quasi-parton distribution functions (quasi-PDFs) have been recently
proposed by Ji. Defined as the matrix elements of equal-time spatial
correlations, they can be computed on the lattice and should reduce to the
standard PDFs when the proton momentum $P_z$ is very large. Since taking the
$P_z\to \infty$ limit is not feasible in lattice simulations, it is essential
to provide guidance for what values of $P_z$ the quasi-PDFs are good
approximations of standard PDFs. Within the framework of the spectator diquark
model, we evaluate both the up and down quarks' quasi-PDFs and standard PDFs
for all leading-twist distributions (unpolarized distribution $f_1$, helicity
distribution $g_1$, and transversity distribution $h_1$). We find that, for
intermediate parton momentum fractions $x$, quasi-PDFs are good approximations
to standard PDFs (within $20-30%$) when $P_z\gtrsim 1.5-2$ GeV. On the other
hand, for large $x\sim 1$ much larger $P_z > 4$ GeV is necessary to obtain a
satisfactory agreement between the two sets. We further test the Soffer
positivity bound, and find that it does not hold in general for quasi-PDFs.
