Left panels: the distribution of N_p for the random test field for K = 2, ε = 0.20 deg (panel a), red solid boxes). The empty blue bar line represents a Poissonian best fit. Panel b) shows K = 2 ε = 0.30 deg (purple solid triangles). Panel c) shows the full K-ε parameter space, the solid black line represent a log-normal best fit. Right panels: panel c) shows the distribution of (black solid line), and its best fit by means of a log-normal distribution (red dashed line). Panel d) shows the N_p distribution for the fake clusters in the sky test field 1 (red solid circles), and the blue empty bars show a Poissonian best fit. Panel e) shows the N_p distribution for the fake clusters in the sky test field 1 (blue hatched histogram), the log-normal best fit (red dashed line), and the Poissonian fit (solid black line).