  We study the errors brought by finite volume effects and dilution effects on
the practical determination of the count probability distribution function
P_N(n,L), which is the probability of having N objects in a cell of volume L^3
for a set of average number density n. Dilution effects are particularly
relevant to the so-called sparse sampling strategy. This work is mainly done in
the framework of the scaling model (Balian \& Schaeffer 1989), which assumes
that the Q-body correlation functions obey the scaling relation xi_Q(K r_1,...,
K r_Q) = K^{-(Q-1) gamma} xi_N(r_1,..., r_Q). We use three synthetic samples as
references to perform our analysis: a fractal generated by a Rayleigh-L\'evy
random walk with 3.10^4 objects, a sample dominated by a spherical power-law
cluster with 3.10^4 objects and a cold dark matter (CDM) universe involving
3.10^5 matter particles.
