3.4 Higher-order Statistics

Given the complexity of the observed large-scale structure, a complete statistical description of the galaxy distribution requires the use of high-order statistics. To investigate high-order correlations, counts-in-cells have been used to compute the count probability distribution function P (N, V), from which the Void Probability Function (VPF), P (0, V), and the normalized skewness S₃ and kurtosis S₄ have been derived. These statistics have been used to test the hierarchical relations and to compare data to simulations using optical and infrared-selected samples with complete redshift information (Vogeley et al. 1991, Lachieze-Rey et al. 1992, Bouchet et al. 1993, Benoist et al. 1998). From the moments of the counts distribution and from the scaling of the VPF one finds that the galaxy distribution satisfies the scaling relations predicted by second-order perturbation theory well into the non-linear regime. However, high-order statistics, such as VPF, have not proven to be good discriminants of different cosmological models. Instead, preliminary results suggest that high order moments may be best used to constrain galaxy biasing models, especially for large redshift samples expected from 2dF and SDSS.