  To probe the weakly non-linear regime, past the point where simple linear
theory is sufficient to describe the statistics of the density distribution, we
measure the skewness (S_3) and kurtosis (S_4) of the Count Probability
Distribution Function (CPDF) of the IRAS 1.2 Jy sample obtained from counts in
cells. These quantities are free parameters in a maximum likelihood fit of an
Edgeworth expansion convolved with a Poissonian to the observed CPDF. This
method, applicable on scales greater than 5 Mpc, is appreciably less sensitive
to the tail of the distribution than are measurements of S_3 and S_4 from
moments of the CPDF. We measure S_3 and S_4 to l~50 h^{-1} Mpc; the data are
consistent with scale invariance, yielding averages of <S_3> = 2.83 +/- 0.09,
and <S_4> = 6.89 +/- 0.68. These values are higher than those found using the
moments method on the same data set, <S_3> = 1.5 +/- 0.5 and <S_4> = 4.4 +/-
3.7, due to lack of correction in the latter work for finite-volume effects.
Unlike the moments method, our results are quite robust to the fact that IRAS
galaxies are under-represented in cluster cores. We use N-body simulations to
show that our method yields unbiased results.
