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To probe the weakly non-linear regime, past the point where simple lineartheory is sufficient to describe the statistics of the density distribution, wemeasure the skewness (S_3) and kurtosis (S_4) of the Count ProbabilityDistribution Function (CPDF) of the IRAS 1.2 Jy sample obtained from counts incells. These quantities are free parameters in a maximum likelihood fit of anEdgeworth expansion convolved with a Poissonian to the observed CPDF. Thismethod, applicable on scales greater than 5 Mpc, is appreciably less sensitiveto the tail of the distribution than are measurements of S_3 and S_4 frommoments of the CPDF. We measure S_3 and S_4 to l~50 h^{-1} Mpc; the data areconsistent 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 themoments 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 IRASgalaxies are under-represented in cluster cores. We use N-body simulations toshow that our method yields unbiased results.

Measuring High‐Order Moments of the Galaxy Distribution from Counts in Cells: The Edgeworth Approximation