Compare methods

	Pareto/NBD Model	Gamma-Gamma Spend Model
Field	Marketing	Marketing
Family	Regression model	Regression model
Year of origin	1987	2013
Originator	David C. Schmittlein, Donald G. Morrison & Richard Colombo	Peter S. Fader & Bruce G. S. Hardie
Type	Probabilistic buy-till-you-die model with continuous-time dropout	Probabilistic model of monetary value per transaction
Seminal source	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.	Fader, P. S., & Hardie, B. G. S. (2013). The Gamma-Gamma Model of Monetary Value. Technical note, www.brucehardie.com/notes/025/.
Aliases	Pareto/NBD, Schmittlein-Morrison-Colombo Model, Counting Your Customers Model, SMC Model	Gamma-Gamma Model, Gamma/Gamma Spend Model, Monetary Value Model, Average Transaction Value Model
Related	4	4
Summary	The Pareto/NBD model is the foundational buy-till-you-die model of customer-base analysis, answering the question of which customers are still active and how many transactions they will make in the future from a non-contractual purchase history. Introduced by David Schmittlein, Donald Morrison and Richard Colombo in their 1987 Management Science paper "Counting Your Customers," it combines two stochastic stories: customers buy according to a Poisson process while alive, and each customer has an unobserved lifetime after which they are permanently inactive. Purchasing rates vary across customers by a gamma distribution, producing the negative binomial (NBD) for counts, and dropout rates also vary by a gamma distribution, producing a Pareto distribution of lifetimes, which gives the model its name. Unlike later discrete-dropout variants, the Pareto/NBD allows a customer to become inactive at any instant in continuous time, not only after a purchase. From only each customer's recency, frequency and tenure, the model yields a probability that the customer is still alive and an expectation of their future buying. Its main cost is computational: estimation involves Gaussian hypergeometric functions and careful numerical integration, which historically made it hard to apply.	The Gamma-Gamma model of monetary value is the standard companion to buy-till-you-die transaction models, estimating how much a customer spends per transaction so that purchase-count forecasts can be turned into monetary customer lifetime value. Formalized by Peter Fader and Bruce Hardie in a widely cited technical note, it assumes that each customer's individual transactions vary around their own average spend according to a gamma distribution, and that these per-customer average-spend levels themselves vary across the population according to a second gamma distribution, giving the model its name. A central assumption is that a customer's monetary value is independent of their transaction frequency, which lets the spend model be estimated and combined separately from a frequency model such as BG/NBD or Pareto/NBD. The model produces, for each customer, a Bayesian estimate of expected spend that shrinks a customer's noisy observed average toward the population mean, with more shrinkage for customers who have made fewer transactions. This guards against over-trusting the average order value of a customer seen only once or twice. The result feeds directly into the residual-lifetime-value calculation that powers customer-base analysis.