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Estimating Heterogeneity in Consumers' Purchase Rates

Author

Listed:
  • Sunil Gupta

    (Columbia University)

  • Donald G. Morrison

    (University of California, Los Angeles)

Abstract

Consumers are different in their purchase rates and it is important to determine this heterogeneity. If a consumer's purchases follow a Poisson process (hence exponential interpurchase time), and purchase rates are distributed gamma across consumers, then a simple measure of heterogeneity is the shape parameter of the gamma distribution. Although we can use either the number of purchases or the interpurchase time data to estimate this heterogeneity, we suggest that number of purchases data are better and easier to use. It is also suggested that while method of moments (MOM) gives good parameter estimates for models using number of purchases data (e.g. NBD), it may be very misleading for models using interpurchase time data (e.g. Pareto). We also recommend caution when using maximum likelihood estimation procedure for the interpurchase time data if multiple observations are available for each consumer. This is to ensure that the model captures heterogeneity across consumers and not across observations.

Suggested Citation

  • Sunil Gupta & Donald G. Morrison, 1991. "Estimating Heterogeneity in Consumers' Purchase Rates," Marketing Science, INFORMS, vol. 10(3), pages 264-269.
    • Handle: RePEc:inm:ormksc:v:10:y:1991:i:3:p:264-269
    DOI: 10.1287/mksc.10.3.264
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    Cited by:

    1. Bruce G. S. Hardie & Peter S. Fader & Robert Zeithammer, 2003. "Forecasting new product trial in a controlled test market environment," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 22(5), pages 391-410.
    2. Schweidel, David A. & Fader, Peter S., 2009. "Dynamic changepoints revisited: An evolving process model of new product sales," International Journal of Research in Marketing, Elsevier, vol. 26(2), pages 119-124.
    3. Alan L. Montgomery, 2001. "Applying Quantitative Marketing Techniques to the Internet," Interfaces, INFORMS, vol. 31(2), pages 90-108, April.
    4. Peter S. Fader & Bruce G. S. Hardie & Chun-Yao Huang, 2004. "A Dynamic Changepoint Model for New Product Sales Forecasting," Marketing Science, INFORMS, vol. 23(1), pages 50-65, October.
    5. Meade, Nigel & Islam, Towhidul, 2010. "Using copulas to model repeat purchase behaviour - An exploratory analysis via a case study," European Journal of Operational Research, Elsevier, vol. 200(3), pages 908-917, February.
    6. Kinshuk Jerath & Peter S. Fader & Bruce G. S. Hardie, 2011. "New Perspectives on Customer "Death" Using a Generalization of the Pareto/NBD Model," Marketing Science, INFORMS, vol. 30(5), pages 866-880, September.

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