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

We measure the skewness (S₃) and kurtosis (S₄) 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 is appreciably less sensitive to the tail of the distribution than are measurements of S₃ and S₄ from moments of the CPDF. We measure S₃ and S₄ to l ~ 50 h^-1 Mpc; the data are consistent with scale invariance, yielding averages of = 2. 83 +/- 0. 06, and = 6. 89 +/- 0. 48. These values are higher than those found using the moments method on the same data set, = 1. 5 +/- 0. 5 and = 4. 4 +/- 3. 7. 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, while the moments method systematically underestimates S₃ and S₄ (abridged).