The range parameters are usually taken from tabulated data, or fit formulae [Sel81], which can be obtained by theoretical calculations sketched in Section 2.1, or they are extracted from experiments (e.g. [Hof75b], [Rys81], [Par90]).
The range parameter can be obtained from experimental data by evaluating the integrals (2.2-5) for the moments. The application of this procedure would lead to moments which represent the data only in the vicinity of the peak, since values off the peak contribute only little to the integral. For realistic simulation the measured profile should be approximated even in an area where the concentration values are several decades below the maximum. This is achieved only by curve fitting on a logarithmic scale with the moments as fit parameters. An algorithm to generate optimized moments for Pearson type distribution functions from Monte Carlo data has been published recently by Bowyer et al. [Bow92].