We apply several statistical estimators to high–resolution N–body simulations of two currently viable cosmological models : a mixed dark matter model , having \Omega _ { \nu } = 0.2 contributed by two massive neutrinos ( C +2 \nu DM ) , and a Cold Dark Matter model with Cosmological Constant ( \Lambda CDM ) with \Omega _ { 0 } = 0.3 and h = 0.7 .
Our aim is to compare simulated galaxy samples with the Perseus–Pisces redshift survey ( PPS ) .
We consider the n –point correlation functions ( n = 2 – 4 ) , the N –count probability functions P _ { N } , including the void probability function P _ { 0 } , and the underdensity probability function U _ { \epsilon } ( where \epsilon fixes the underdensity threshold in percentage of the average ) .
We find that P _ { 0 } ( for which PPS and CfA2 data agree ) and P _ { 1 } distinguish efficiently between the models , while U _ { \epsilon } is only marginally discriminatory .
On the contrary , the reduced skewness and kurtosis are , respectively , S _ { 3 } \simeq 2.2 and S _ { 4 } \simeq 6 –7 in all cases , quite independent of the scale , in agreement with hierarchical scaling predictions and estimates based on redshift surveys .
Among our results , we emphasize the remarkable agreement between PPS data and C +2 \nu DM in all the tests performed .
In contrast , the above \Lambda CDM model has serious difficulties in reproducing observational data if galaxies and matter overdensities are related in a simple way .