Counts-in-cells analysis of the statistical distribution in an N-body simulated universe

Evolution of the statistical distribution of density field is investigated by means of a counts-in-cells method in a low-density cold-dark-matter simulated universe. Four theoretical distributions, i.e. the negative binomial distribution, the lognormal distribution, the Edgeworth series and the skewed lognormal distribution, are tested to fit the calculated distribution function, and it is shown that only the skewed lognormal distribution of second and third order can describe the evolution of the statistical distribution perfectly well from the initially Gaussian regime to the present stage. The effects of sparse sampling is also investigated and it is discussed that one should use a sample with number density of galaxies larger than $\sim 0.01h^3$Mpc$^{-3}$ in order to recover underlying density distribution.

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