Marketing Letters

, Volume 26, Issue 2, pp 165–173 | Cite as

A simple heuristic for obtaining pareto/NBD parameter estimates

  • Pablo MarshallEmail author


In an influential study, Schmittlein et al. (1987) proposed the pareto/negative binomial distribution (P/NBD) model to predict purchase behavior of customers. Despite its recognized relevance, this model has some drawbacks as follows: (1) it does not allow a zero transaction rate, (2) it assumes convenient but not necessarily realistic gamma distributions for the transaction and drop-out rates across customers, and (3) the estimation procedure requires complicated computations. The purpose of this study is to relax the assumption that purchases and drop-out rates are distributed according to a gamma distribution and propose a simple estimation procedure for the individual parameters that can be applied even if the number of customers is large. A simulation exercise and empirical applications to real datasets compare the simple model proposed with the P/NBD model. The results show that the simple procedure is better in cases where the number of transactions and/or the observation period is large.


Prediction consumer behavior Nonparametric model Pareto NBD model 


  1. Batislam, E. P., Denizel, M., & Filiztekin, A. (2007). Empirical validation and comparison of models for customer base analysis. Internat. J. Res. Marketing, 24(3), 201–209.CrossRefGoogle Scholar
  2. Bemmaor, A. C., & Glady, N. (2012). Modeling purchasing behavior with sudden death: a flexible customer lifetime model. Management Science, 58(5), 1012–1102.CrossRefGoogle Scholar
  3. Ehrenberg, A. S. C. (1988). Repeat Buying (2nd ed.). New York: Oxford University Press.Google Scholar
  4. Fader, P.S., & Hardie, B.G.S. (2001). Forecasting Repeat Sales at CDNOW: A Case Study. Part 2 of 2. Interfaces 31(May–June) S94–S107.Google Scholar
  5. Fader, P.S., & Hardie, B.G.S. (2005). A Note on Deriving the Pareto/NBD Model and Related Expressions.
  6. Fader, P. S., Hardie, B. G. S., & Lee, K. L. (2005b). Counting your customers the easy way: an alternative to the Pareto/NBD model. Marketing Science, 24(3), 275–284.CrossRefGoogle Scholar
  7. Jerath, K., Fader, P. S., & Hardie, B. G. S. (2011). New perspectives on customer death. Using a generalization of the Pareto/NBD model. Marketing Science, 30(5), 866–880.CrossRefGoogle Scholar
  8. Ma, S.H., & Liu, J.L. (2007). The MCMC Approach for Solving the Pareto/NBD Model and Possible Extensions, Proceedings of the Third International Conference on Natural.Google Scholar
  9. Reinartz, W., & Kumar, V. (2002). The Mismanagement of Customer Loyalty. Harvard Business Review (July), pp. 86–97.Google Scholar
  10. Schmittlein, D. C., Morrison, D. G., & Colombo, R. (1987). Counting your customers: who are they and what will they do next? Management Science, 33(1), 1–24.CrossRefGoogle Scholar
  11. Singh, S. S., Borle, S., & Jain, D. C. (2009). A generalized framework for estimating customer lifetime value when customer lifetimes are not observed. Quant Marketing Economy, 7(2), 181–205.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Escuela de AdministraciónPontificia Universidad Católica de ChileSantiagoChile

Personalised recommendations