**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
*S*_{3} and
kurtosis *S*_{4} 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.