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Predicting Future Random Events Based on Past Performance

Author

Listed:
  • Donald G. Morrison

    (Columbia University)

  • David C. Schmittlein

    (University of Pennsylvania)

Abstract

There are many situations where one is interested in predicting the expected number of events in period 2 given that x events occurred in period 1. For example, insurance companies must decide whether or not to cancel the insurance of drivers who had 3 or more accidents during the previous year. In analyzing marketing research data an analyst may wish to predict the number of future purchases to be made by those customers who made x purchases in the previous 3 months. The owner of a baseball team may wish to estimate the number of home runs a batter will hit this year given he hit (say) 40 home runs last year. When the events (e.g., accidents, purchase occasions, home runs) can be assumed to occur randomly over time a very general result due to Robbins (Robbins, H. 1977. Prediction and estimation for the compound Poisson distribution. Proc. National Acad Sci. USA 74 2670--2671.) is available. This approach has certain advantages and disadvantages with respect to the negative binomial model that is commonly used to analyze purchasing and accident data. The Robbins result is particularly appropriate for predicting what the zero class in period 1 will do in period 2. The main purpose of this paper is to present the Robbins result in a form that can be readily understood by applied researchers in a variety of disciplines. Data on consumer purchases, motor vehicle violations and accidents are analyzed and applications to other areas are discussed.

Suggested Citation

  • Donald G. Morrison & David C. Schmittlein, 1981. "Predicting Future Random Events Based on Past Performance," Management Science, INFORMS, vol. 27(9), pages 1006-1023, September.
    • Handle: RePEc:inm:ormnsc:v:27:y:1981:i:9:p:1006-1023
    DOI: 10.1287/mnsc.27.9.1006
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    Citations

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    Cited by:

    1. Trinh, Giang & Wright, Malcolm J., 2022. "Predicting future consumer purchases in grocery retailing with the condensed Poisson lognormal model," Journal of Retailing and Consumer Services, Elsevier, vol. 64(C).
    2. Michael Braun & André Bonfrer, 2011. "Scalable Inference of Customer Similarities from Interactions Data Using Dirichlet Processes," Marketing Science, INFORMS, vol. 30(3), pages 513-531, 05-06.
    3. Michael Braun & Wendy W. Moe, 2013. "Online Display Advertising: Modeling the Effects of Multiple Creatives and Individual Impression Histories," Marketing Science, INFORMS, vol. 32(5), pages 753-767, September.
    4. Jeongwen Chiang & Ching-Fan Chung & Emily Cremers, 2001. "Promotions and the pattern of grocery shopping time," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(7), pages 801-819.
    5. Indranil Bardhan & Jeong-ha (Cath) Oh & Zhiqiang (Eric) Zheng & Kirk Kirksey, 2015. "Predictive Analytics for Readmission of Patients with Congestive Heart Failure," Information Systems Research, INFORMS, vol. 26(1), pages 19-39, March.
    6. Rosenfield, Donald B., 1947-, 1985. "Framework for predicting frequencies of events," Working papers 1662-85., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    7. 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.
    8. Baek Jung Kim & Vishal Singh & Russell S. Winer, 2017. "The Pareto rule for frequently purchased packaged goods: an empirical generalization," Marketing Letters, Springer, vol. 28(4), pages 491-507, December.
    9. Chen, Zhiyuan & Liang, Xiaoying & Xie, Lei, 2016. "Inter-temporal price discrimination and satiety-driven repeat purchases," European Journal of Operational Research, Elsevier, vol. 251(1), pages 225-236.
    10. Young-Hoon Park & Peter S. Fader, 2004. "Modeling Browsing Behavior at Multiple Websites," Marketing Science, INFORMS, vol. 23(3), pages 280-303, May.
    11. Steven Miller & Eric Bradlow & Kevin Dayaratna, 2006. "Closed-form Bayesian inferences for the logit model via polynomial expansions," Quantitative Marketing and Economics (QME), Springer, vol. 4(2), pages 173-206, June.
    12. Teck-Hua Ho & Young-Hoon Park & Yong-Pin Zhou, 2006. "Incorporating Satisfaction into Customer Value Analysis: Optimal Investment in Lifetime Value," Marketing Science, INFORMS, vol. 25(3), pages 260-277, 05-06.
    13. Anesbury, Zachary William & Talbot, Danielle & Day, Chanel Andrea & Bogomolov, Tim & Bogomolova, Svetlana, 2020. "The fallacy of the heavy buyer: Exploring purchasing frequencies of fresh fruit and vegetable categories," Journal of Retailing and Consumer Services, Elsevier, vol. 53(C).
    14. 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.
    15. Fader, Peter S. & Hardie, Bruce G. S., 2002. "A note on an integrated model of customer buying behavior," European Journal of Operational Research, Elsevier, vol. 139(3), pages 682-687, June.
    16. Bockenholt, Ulf, 1998. "Mixed INAR(1) Poisson regression models: Analyzing heterogeneity and serial dependencies in longitudinal count data," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 317-338, November.
    17. John W. Bradford & Paul K. Sugrue, 1991. "Inventory rotation policies for slow moving items," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(1), pages 87-105, February.
    18. Reutterer, Thomas & Platzer, Michael & Schröder, Nadine, 2021. "Leveraging purchase regularity for predicting customer behavior the easy way," International Journal of Research in Marketing, Elsevier, vol. 38(1), pages 194-215.

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