This article integrates the size of the household into the Negative Binomial Distribution (NBD) to capture the distributions of the number of purchases within groups of households of a given size. Tested on two markets of consumer goods, the model provides predictions that are comparable to those given by separate NBD models.
BEMMAOR, A.C. (1980). A Family-Size Dependent Stochastic Model of Purchase Incidence. In: Proceedings of ORSA/TIMS Special Interest Conference, R. P. Leone, ed., TIMS College on Marketing and The Institute of Management Sciences, pp. 63-67.