Counting your customers from an “always a share” perspective

Models based on the Pareto/NBD framework are among the most popular for customer base analysis. The Pareto/NBD framework assumes that purchasing follows a Poisson process until the customers defect. Therefore, models based on this framework may systematically underestimate the number of future transactions from customers whose probability of returning is greater than zero. In this paper, we propose a new model which assumes that customers do not defect, but instead switch freely between an active and an inactive state. We call this model the “interrupted Poisson process”. According to the model, customers purchase through a Poisson process when they are active and they do not purchase when they are inactive. Bayesian simulation methods for parameter estimation are developed and implemented via a Markov chain Monte Cacrlo (MCMC) simulation. Several useful expressions for customer base analysis are derived. Through simulation experiments, we show that the rate of customers moving from an inactive to an active state is an important factor determining the fit and predictive ability of the Pareto/NBD model and our model. An empirical analysis, using two real-life datasets, demonstrates the superior performance of the proposed model.