IDEAS home Printed from
   My bibliography  Save this article

“Counting Your Customers” One by One: A Hierarchical Bayes Extension to the Pareto/NBD Model


  • Makoto Abe

    () (Graduate School of Economics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan)


This research extends a Pareto/NBD model of customer-base analysis using a hierarchical Bayesian (HB) framework to suit today's customized marketing. The proposed HB model presumes three tried and tested assumptions of Pareto/NBD models: (1) a Poisson purchase process, (2) a memoryless dropout process (i.e., constant hazard rate), and (3) heterogeneity across customers, while relaxing the independence assumption of the purchase and dropout rates and incorporating customer characteristics as covariates. The model also provides useful output for CRM, such as a customer-specific lifetime and survival rate, as by-products of the MCMC estimation. Using three different types of databases—music CD for e-commerce, FSP data for a department store and a music CD chain, the HB model is compared against the benchmark Pareto/NBD model. The study demonstrates that recency-frequency data, in conjunction with customer behavior and characteristics, can provide important insights into direct marketing issues, such as the demographic profile of best customers and whether long-life customers spend more.

Suggested Citation

  • Makoto Abe, 2009. "“Counting Your Customers” One by One: A Hierarchical Bayes Extension to the Pareto/NBD Model," Marketing Science, INFORMS, vol. 28(3), pages 541-553, 05-06.
  • Handle: RePEc:inm:ormksc:v:28:y:2009:i:3:p:541-553

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Peter S. Fader & Bruce G. S. Hardie & Ka Lok Lee, 2005. "“Counting Your Customers” the Easy Way: An Alternative to the Pareto/NBD Model," Marketing Science, INFORMS, vol. 24(2), pages 275-284, August.
    2. Young-Hoon Park & Peter S. Fader, 2004. "Modeling Browsing Behavior at Multiple Websites," Marketing Science, INFORMS, vol. 23(3), pages 280-303, May.
    3. Füsun F. Gönül & Frenkel Ter Hofstede, 2006. "How to Compute Optimal Catalog Mailing Decisions," Marketing Science, INFORMS, vol. 25(1), pages 65-74, 01-02.
    4. Roland T. Rust & Tuck Siong Chung, 2006. "Marketing Models of Service and Relationships," Marketing Science, INFORMS, vol. 25(6), pages 560-580, 11-12.
    5. Baohong Sun, 2006. "—Technology Innovation and Implications for Customer Relationship Management," Marketing Science, INFORMS, vol. 25(6), pages 594-597, 11-12.
    6. David C. Schmittlein & Donald G. Morrison & Richard Colombo, 1987. "Counting Your Customers: Who-Are They and What Will They Do Next?," Management Science, INFORMS, vol. 33(1), pages 1-24, January.
    7. David C. Schmittlein & Robert A. Peterson, 1994. "Customer Base Analysis: An Industrial Purchase Process Application," Marketing Science, INFORMS, vol. 13(1), pages 41-67.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Peter S. Fader & Bruce G. S. Hardie & Jen Shang, 2010. "Customer-Base Analysis in a Discrete-Time Noncontractual Setting," Marketing Science, INFORMS, vol. 29(6), pages 1086-1108, 11-12.
    2. Huang, Chun-Yao, 2012. "To model, or not to model: Forecasting for customer prioritization," International Journal of Forecasting, Elsevier, vol. 28(2), pages 497-506.
    3. Makoto Abe, 2015. "Deriving Customer Lifetime Value from RFM Measures:Insights into Customer Retention and Acquisition," CIRJE F-Series CIRJE-F-962, CIRJE, Faculty of Economics, University of Tokyo.
    4. Juha Karvanen & Ari Rantanen & Lasse Luoma, 2014. "Survey data and Bayesian analysis: a cost-efficient way to estimate customer equity," Quantitative Marketing and Economics (QME), Springer, vol. 12(3), pages 305-329, September.
    5. Shaohui Ma & Joachim Büschken, 2011. "Counting your customers from an “always a share” perspective," Marketing Letters, Springer, vol. 22(3), pages 243-257, September.
    6. repec:eee:ijrema:v:32:y:2015:i:1:p:78-93 is not listed on IDEAS
    7. repec:tiu:tiutis:52e91e47-4a2d-4e7b-bb23-3926b842ae30 is not listed on IDEAS
    8. repec:eee:ijrema:v:31:y:2014:i:3:p:266-279 is not listed on IDEAS
    9. Song, Tae Ho & Kim, Sang Yong & Kim, Ji Yoon, 2016. "The dynamic effect of customer equity across firm growth: The case of small and medium-sized online retailers," Journal of Business Research, Elsevier, vol. 69(9), pages 3755-3764.
    10. Giang Trinh & Cam Rungie & Malcolm Wright & Carl Driesener & John Dawes, 2014. "Predicting future purchases with the Poisson log-normal model," Marketing Letters, Springer, vol. 25(2), pages 219-234, June.
    11. Hoppe, Daniel & Wagner, Udo, 2014. "The role of lifetime activity cues in customer base analysis," Journal of Business Research, Elsevier, vol. 67(5), pages 983-989.
    12. Liu, Fan & Hua, Zhongsheng & Lim, Andrew, 2015. "Identifying future defaulters: A hierarchical Bayesian method," European Journal of Operational Research, Elsevier, vol. 241(1), pages 202-211.
    13. Jerath, Kinshuk & Fader, Peter S. & Hardie, Bruce G.S., 2016. "Customer-base analysis using repeated cross-sectional summary (RCSS) data," European Journal of Operational Research, Elsevier, vol. 249(1), pages 340-350.
    14. Leslie Hannah & Makoto Kasuya, 2015. "Twentieth Century Enterprise Forms: Japan in Comparative Perspective," CIRJE F-Series CIRJE-F-966, CIRJE, Faculty of Economics, University of Tokyo.
    15. Albert C. Bemmaor & Nicolas Glady, 2012. "Modeling Purchasing Behavior with Sudden "Death": A Flexible Customer Lifetime Model," Management Science, INFORMS, vol. 58(5), pages 1012-1021, May.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormksc:v:28:y:2009:i:3:p:541-553. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.