Customer-Base Analysis in a Discrete-Time Noncontractual Setting

48 Pages Posted: 6 Apr 2009 Last revised: 9 May 2011

See all articles by Peter Fader

Peter Fader

University of Pennsylvania - Marketing Department

Bruce Hardie

London Business School

Jen Shang

Indiana University

Date Written: October 29, 2009


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 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 dataset on donations made by the supporters of a public radio station 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.

Keywords: BG/BB, beta-geometric, beta-binomial, customer-base analysis, customer lifetime value, CLV, RFM, Pareto/NBD

Suggested Citation

Fader, Peter and Hardie, Bruce and Shang, Jen, Customer-Base Analysis in a Discrete-Time Noncontractual Setting (October 29, 2009). Available at SSRN: or

Peter Fader (Contact Author)

University of Pennsylvania - Marketing Department ( email )

700 Jon M. Huntsman Hall
3730 Walnut Street
Philadelphia, PA 19104-6340
United States

Bruce Hardie

London Business School ( email )

Regent's Park
London, NW1 4SA
United Kingdom

Jen Shang

Indiana University ( email )

107 S Indiana Ave
100 South Woodlawn
Bloomington, IN 47405
United States

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