Modeling Purchasing Behavior with Sudden “Death”: A Flexible Customer Lifetime Model

This study proposes a new customer lifetime model: the gamma/Gompertz distribution (G/G). The advantage of this model relative to the well-known Pareto distribution is twofold: (i) its probability density function can exhibit a mode at zero or an interior mode, and (ii) it can be skewed to the right or to the left. We combine the G/G with a negative binomial distribution (NBD) and obtain the moments of the distribution of the number of transactions over (0, T] and (T, T+T * ]. Out of six data sets, the G/G/NBD model provides a notable improvement in the log-likelihood over the Pareto/NBD model in four data sets. It can indicate substantial differences in expected residual lifetimes compared to the Pareto/NBD and induce a retention rather than acquisition policy. On the average, the G/G/NBD exhibits slightly better forecasts of the mean number of transactions than the Pareto/NBD. This paper was accepted by Pradeep Chintagunta, marketing.