The Normalizing Constant in the BG/BB Model

4 Pages Posted: 12 Sep 2018 Last revised: 13 Nov 2018

See all articles by Daniel McCarthy

Daniel McCarthy

Emory University - Department of Marketing

Michael Braun

Southern Methodist University (SMU) - Marketing Department

Arun Gopalakrishnan

Washington University in St. Louis - John M. Olin Business School

Date Written: September 18, 2018

Abstract

This note provides a clarification regarding the conditional and marginal likelihood functions in the BG/BB model, as published in Marketing Science by Fader, Hardie, and Shang (2010). Their Equations 4 and 5 do not include normalizing constants which, if included, would equate these likelihood functions with their corresponding joint probability functions. While these expressions are valid, because likelihood functions need only be correct up to a constant of proportionality, they are not joint probability functions, which may be a source of potential confusion for users who mistakenly equate the one for the other. Assuming the likelihood functions in Equations 4 and 5 are equal to their respective joint probability functions will lead to an incorrect joint probability distribution over recency and frequency data, resulting in incorrect goodness-of-fit metrics and managerially relevant expressions. We provide formal derivations of the joint probability functions that correspond to the likelihood functions in Equations 4 and 5 to remove this potential source of confusion for users of the BG/BB model.

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

JEL Classification: M31

Suggested Citation

McCarthy, Daniel and Braun, Michael and Gopalakrishnan, Arun, The Normalizing Constant in the BG/BB Model (September 18, 2018). SMU Cox School of Business Research Paper No. 18-33. Available at SSRN: https://ssrn.com/abstract=3241680 or http://dx.doi.org/10.2139/ssrn.3241680

Daniel McCarthy

Emory University - Department of Marketing ( email )

Goizueta Business School
1300 Clifton Road
Atlanta, GA 30322
United States

Michael Braun (Contact Author)

Southern Methodist University (SMU) - Marketing Department ( email )

United States

Arun Gopalakrishnan

Washington University in St. Louis - John M. Olin Business School ( email )

One Brookings Drive
Campus Box 1133
St. Louis, MO 63130-4899
United States

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