Introduction and Background
The negative binomial distribution (NBD) has been widely used in marketing to model purchase frequency counts, particularly in the packaged goods context. It is known as one of the true marketing laws (Ehrenberg, 1996; Sharp, 2010), and was first applied to marketing science by Ehrenberg (1959) to model brand purchasing behavior. Ehrenberg made two assumptions: (a) Purchases of a given consumer in successive time periods follow a Poisson distribution. This implies that the variance of purchases within individual consumers is "as if" random over time (i.e., Poisson process). (b) The mean rates of purchasing of different consumers...