A generating process In Chapter 2 we made some general assumptions concerning the distribution of X = (X1,X2,…,XS) stating that the probability generating function of X was $$ {{G}_{x}}\left( z \right) = {{M}_{v}}\left( {\Sigma {{p}_{i}}{{z}_{i}} - 1} \right), $$ where Mv( ) denotes some moment-generating function. We now proceed to closer examination of what this assumption means in practice. We shall let the individuals be symbolized by points in a plane; let Ω denote the part of the plane defining the population to be investigated. The sampling of individuals is carried out by placing some area, say a circle or a quadrat, at random in Ω and counting the number of individuals belonging to the various species in this area.