New Perspectives on Customer “Death” Using a Generalization of the Pareto/NBD Model

New Perspectives on Customer “Death” Using a Generalization of the Pareto/NBD Model Several researchers have proposed models of buyer behavior in noncontractual settings which assume that customers are “alive” for some period of time, then become permanently inactive. The best-known such model is the Pareto/NBD, which assumes that customer attrition (dropout or “death”) can occur at any point in calendar time. A recent alternative model, the BG/NBD, assumes that customer attrition follows a Bernoulli “coin-flipping” process that occurs after every purchase occasion. While the modification results in a model that is much easier to implement, it means that heavy buyers have more opportunities to “die.” In this paper, we develop a model with a discrete-time dropout process tied to calendar time. Specifically, we assume that every customer periodically “flips a coin” to determine whether she “drops out” or continues as a customer. For the purchasing while “alive” component, we maintain the assumptions of the Pareto/NBD and BG/NBD models. This results in a model that has the appealing characteristics of the Pareto/NBD with none of its computational burden. This periodic death opportunity (PDO) model allows us to take a closer look at how assumptions about customer death influence model fit. When the time period after which each customer makes his or her dropout decision (which we call periodicity) is very small, we show analytically that the PDO model converges to the Pareto/NBD. When the periodicity is longer than the calibration period, the dropout process is “shut off” and the PDO model converges to the NBD model. By systematically varying the periodicity between these limits, we can explore the full spectrum of models between the “continuous-time death” Pareto/NBD and the näıve “no death” NBD. In covering this spectrum, the PDO model performs at least as well as either of these models; we show this theoretically and our empirical analysis demonstrates the superior performance of the PDO model on two datasets. Finally, we extend the basic model to allow for heterogeneity in periodicity across customers and find that such an extension confirms the results of the basic model.