MEASURING HIGH-ORDER MOMENTS OF THE GALAXY DISTRIBUTION FROM COUNTS IN CELLS - THE EDGEWORTH APPROXIMATION

To probe the weakly nonlinear regime, past the point where simple line ar theory is sufficient to describe the statistics of the density dist ribution, we measure the skewness (S-3) and kurtosis (S-4) of the coun t probability distribution function (CPDF) of the IRAS 1.2 Jy sample o btained from counts in cells. These quantities are free parameters in a maximum likelihood fit of an Edgeworth expansion convolved with a Po issonian to the observed CPDF. This method, applicable on scales great er than or similar to 5 h(-1) Mpc, is appreciably less sensitive to th e tail of the distribution than are measurements of S-3 and S-4 from m oments of the CPDF. We measure S-3 and S-4 to l similar to 50 h(-1) Mp c; 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 hig her than those found by Bouchet et al, in 1993 ([S-3] = 1.5 +/- 0.5 an d [S-4] = 4.4 +/- 3.7) using the moments method on the same data set, owing to lack of correction for finite-volume effects in the latter wo rk. Unlike the moments method, our results are quite robust to the fac t that IRAS galaxies are underrepresented in cluster cores. We use N-b ody simulations to show that our method yields unbiased results.