Customer-Base Analysis in a Discrete-Time Non-contractual Setting



Many businesses track repeat transactions on a discrete-time basis. These include: (1) companies where transactions can only occur at fixed regular intervals, (2) firms that frequently associate transactions with specific events (e.g., a charity that records whether or not supporters respond to a particular appeal), and (3) organizations that simply use discrete reporting periods even though the transactions can occur at any time. Furthermore, many of these businesses operate in a non-contractual 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 behavioural 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 behaviour (and other quantities of managerial interest). We apply this discrete-time analog of the well-known Pareto/NBD model to a dataset on donations made by the supporters of a charity located in the Midwestern United States. Our analysis demonstrates the excellent ability of the BG/BB model to describe and predict the future behaviour of a customer base.
Bruce Hardie is Professor of Marketing at London Business School. He holds B.Com and M.Com degrees from the University of Auckland (New Zealand), and MA and PhD degrees from the University of Pennsylvania.
His primary research interest lies in the development of data-based models to support marketing analysts and decision makers, with a particular interest in models that are easy to implement. Most of his current projects focus on the development of probability models for customer-base analysis. Bruce's research has appeared in various marketing, operations research and statistics journals, and he currently serves on the editorial boards of the International Journal of Research in Marketing, the Journal of Interactive Marketing, and Marketing Science.
Contact information:
Dr. S. Puntoni