  We perform a detailed investigation of the statistical properties of the
projected distribution of galaxy clusters obtained in Cold Dark Matter (CDM)
models with both Gaussian and skewed primordial density fluctuations. We use
N-body simulations to construct a set artificial Lick maps. An objective
cluster--finding algorithm is used to identify clusters of different richness.
For Gaussian models, the overall number of clusters is too small in the
standard CDM case, but a model with higher normalisation fares much better;
non--Gaussian models with negative skewness also fit faily well. We apply
several statistical tests to compare real and simulated cluster samples, such
as the 2-point correlation function, the minimal spanning tree construction,
the multifractal analysis and the skewness of cell counts. The emerging picture
is that Gaussian models, even with a higher normalization, are in trouble.
Skew-positive models are also ruled out, while skew-negative models can
reproduce the observed clustering of galaxy clusters in the CDM framework.
