A Comparison of some Stochastic Models of Interpurchase Intervals and of Aggregate Purchase Incidence

SYNOPTIC ABSTRACT

The objective of this paper is to shed some light on whether the choice of a stochastic model for modeling purchase incidence is crucial. Specifically, we theoretically and empirically evaluate several stochastic models of interpurchase intervals at the individual level and purchase incidence at the aggregate level. We compare the exponential, Erlang-2, gamma, lognormal, Weibull, and inverse Gaussian distributions as models of individual level interpurchase intervals. For models of aggregate level purchase incidence, we evaluate the Negative Binomial Distribution (NBD), the Compound Inverse Gaussian (CIG), and the Generalized Poisson Distribution (GPD). Our results indicate that even though the two parameter gamma distribution is by and large the best at the individual level, the exponential distribution is a close competitor. At the aggregate level, the complex CIG does not perform as well as the NBD and the GPD.

Keywords and phrases:

• Marketing Models
• Probability Distributions
• Stochastic Models