Structure and formation of superclusters. XIII - The void probability function

The void probability function (VPF) has been calculated for a number of real, model, random cluster and Poisson samples. The VPF has been studied for scaling properties, for dependence on the bias threshold density (in case of model samples), and for other factors influencing the quantitative comparison of models with observations. The VPF of both real and model samples depends on the number of galaxies and the size of samples. This dependence is not an artefact of the method but reflects continuous changes in the weak structure in low-density regions due to the gradual decay of small systems with decreasing number of galaxies in samples. The VPF is the only statistic used so far which is very sensitive to the presence of weak structures in the sample. It is demonstrated that the scaling properties of the VPF are richer than was thought. In a certain scale interval, the VPF is self-similar, i.e. it has a fractal scaling.