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Modeling Purchasing Behavior with Sudden "Death": A Flexible Customer Lifetime Model

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  • Albert C. Bemmaor

    (ESSEC Business School, 95021 Cergy-Pontoise Cedex, France)

  • Nicolas Glady

    (ESSEC Business School, 95021, Cergy-Pontoise Cedex, France)

Abstract

This study proposes a new customer lifetime model: the gamma/Gompertz distribution (G/G). The advantage of this model relative to the well-known Pareto distribution is twofold: (i) its probability density function can exhibit a mode at zero or an interior mode, and (ii) it can be skewed to the right or to the left. We combine the G/G with a negative binomial distribution (NBD) and obtain the moments of the distribution of the number of transactions over (0, T ] and ( T , T + T * ]. Out of six data sets, the G/G/NBD model provides a notable improvement in the log-likelihood over the Pareto/NBD model in four data sets. It can indicate substantial differences in expected residual lifetimes compared to the Pareto/NBD and induce a retention rather than acquisition policy. On the average, the G/G/NBD exhibits slightly better forecasts of the mean number of transactions than the Pareto/NBD. This paper was accepted by Pradeep Chintagunta, marketing.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:58:y:2012:i:5:p:1012-1021
    DOI: 10.1287/mnsc.1110.1461
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    References listed on IDEAS

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    Cited by:

    1. Darren Shannon & Grigorios Fountas, 2021. "Extending the Heston Model to Forecast Motor Vehicle Collision Rates," Papers 2104.11461, arXiv.org, revised May 2021.
    2. Lydia Simon & Jost Adler, 2022. "Worth the effort? Comparison of different MCMC algorithms for estimating the Pareto/NBD model," Journal of Business Economics, Springer, vol. 92(4), pages 707-733, May.
    3. Naoki Aizawa & Hanming Fang, 2020. "Equilibrium Labor Market Search and Health Insurance Reform," Journal of Political Economy, University of Chicago Press, vol. 128(11), pages 4258-4336.
    4. Mahmoud Aldeni & Carl Lee & Felix Famoye, 2017. "Families of distributions arising from the quantile of generalized lambda distribution," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-18, December.
    5. Heba Soltan Mohamed & M. Masoom Ali & Haitham M. Yousof, 2023. "The Lindley Gompertz Model for Estimating the Survival Rates: Properties and Applications in Insurance," Annals of Data Science, Springer, vol. 10(5), pages 1199-1216, October.
    6. Naoki Aizawa & Hanming Fang, 2015. "Equilibrium Labor Market Search and Health Insurance Reform, Second Version," PIER Working Paper Archive 15-024, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 28 Jun 2015.
    7. Hanming Fang & Andrew J. Shephard, 2019. "Household Labor Search, Spousal Insurance, and Health Care Reform," NBER Working Papers 26350, National Bureau of Economic Research, Inc.
    8. Sharad Borle & Siddharth Singh & Dipak Jain & Ashutosh Patil, 2016. "Analyzing Recurrent Customer Purchases and Unobserved Defections: a Bayesian Data Augmentation Scheme," Customer Needs and Solutions, Springer;Institute for Sustainable Innovation and Growth (iSIG), vol. 3(1), pages 11-28, March.
    9. Shahram Yaghoobzadeh, 2017. "A new generalization of the Marshall–Olkin Gompertz distribution," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 1580-1587, November.
    10. M. S. Eliwa & Ziyad Ali Alhussain & M. El-Morshedy, 2020. "Discrete Gompertz-G Family of Distributions for Over- and Under-Dispersed Data with Properties, Estimation, and Applications," Mathematics, MDPI, vol. 8(3), pages 1-26, March.
    11. Rashad A. R. Bantan & Farrukh Jamal & Christophe Chesneau & Mohammed Elgarhy, 2021. "Theory and Applications of the Unit Gamma/Gompertz Distribution," Mathematics, MDPI, vol. 9(16), pages 1-22, August.
    12. Sharad Borle & Siddharth Shekhar Singh & Dipak C. Jain & Ashutosh Patil, 2016. "Analyzing Recurrent Customer Purchases and Unobserved Defections: a Bayesian Data Augmentation Scheme," Customer Needs and Solutions, Springer;Institute for Sustainable Innovation and Growth (iSIG), vol. 3(1), pages 11-28, March.
    13. Michael Platzer & Thomas Reutterer, 2016. "Ticking Away the Moments: Timing Regularity Helps to Better Predict Customer Activity," Marketing Science, INFORMS, vol. 35(5), pages 779-799, September.
    14. Shama, M.S. & Dey, Sanku & Altun, Emrah & Afify, Ahmed Z., 2022. "The Gamma–Gompertz distribution: Theory and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 689-712.
    15. Pablo Marshall, 2015. "A simple heuristic for obtaining pareto/NBD parameter estimates," Marketing Letters, Springer, vol. 26(2), pages 165-173, June.

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