Customer‐Base Analysis in a Discrete‐Time Noncontractual Setting

Many businesses track repeat transactions on a discrete‐time basis. These include (1) companies for whom transactions can only occur at fixed regular intervals, (2) firms that frequently associate transactions with specific events (e.g., a charity that records whether supporters respond to a particular appeal), and (3) organizations that choose to utilize discrete reporting periods even though the transactions can occur at any time. Furthermore, many of these businesses operate in a noncontractual setting, so they have a difficult time differentiating between those customers who have ended their relationship with the firm versus those who are in the midst of a long hiatus between transactions. We develop a model to predict future purchasing patterns for a customer base that can be described by these structural characteristics. Our beta‐geometric/beta‐Bernoulli (BG/BB) model captures both of the underlying behavioral processes (i.e., customers' purchasing while ‘alive’ and time until each customer permanently ‘dies’). The model is easy to implement in a standard spreadsheet environment and yields relatively simple closed‐form expressions for the expected number of future transactions conditional on past observed behavior (and other quantities of managerial interest). We apply this discrete‐time analog of the well‐known Pareto/NBD model to a data set on donations made by the supporters of a nonprofit organization located in the midwestern United States. Our analysis demonstrates the excellent ability of the BG/BB model to describe and predict the future behavior of a customer base.