  Perturbation theory makes it possible to calculate the probability
distribution function (PDF) of the large scale density field in the small
variance limit. For top hat smoothing and scale-free Gaussian initial
fluctuations, the result depends only on the linear variance, sigma_linear, and
its logarithmic derivative with respect to the filtering scale
-(n_linear+3)=dlog sigma_linear^2/dlog L (Bernardeau 1994). In this paper, we
measure the PDF and its low-order moments in scale-free simulations evolved
well into the nonlinear regime and compare the results with the above
predictions, assuming that the spectral index and the variance are adjustable
parameters, n_eff and sigma_eff=sigma, where sigma is the true, nonlinear
variance. With these additional degrees of freedom, results from perturbation
theory provide a good fit of the PDFs, even in the highly nonlinear regime. The
value of n_eff is of course equal to n_linear when sigma << 1, and it decreases
with increasing sigma. A nearly flat plateau is reached when sigma >> 1. In
this regime, the difference between n_eff and n_linear increases when n_linear
decreases. For initial power-spectra with n_linear=-2,-1,0,+1, we find n_eff ~
-9,-3,-1,-0.5 when sigma^2 ~ 100.
