  We test tree-level perturbation theory for Gaussian initial conditions with
power spectra $P(k)\propto k^n$ by comparing the probability distribution
function (PDF) for the density predicted by the Local Lagrangian Approximation
(LLA) with the results of numerical gravitational clustering simulations. Our
results indicate that our approximation correctly reproduces the evolved
density PDF for $-3 \leq n \leq-1$ power spectra up to the weakly nonlinear
regime, while it shows marginal agreement for power indices n=0 and +1 in the
linear regime and poor agreement beyond this point. This suggests that
tree-level perturbation theory (as realized in the Local Lagrangian
Approximation) can accurately predict the density distribution function for $-3
\leq n \leq -1$ but fails for $n \ge 0$.
