In fitting the NBD Dirichlet model to consumer purchase data the S parameter requires complicated calculation and has no obvious meaning unlike the other three required parameters.
Examination of consumer panel data for many product categories shows the S parameter to be highly correlated with the average number of brands bought. It may therefore be interpreted as a measure of diversity of brand purchasing behaviour in the category.
Bound, J (2009), "The S Parameter in the Dirichlet-NBD Model: a Simple Interpretation", Journal of Empirical Generalisations in Marketing Science, Vol. 12, No. 3