Gamma-Gamma Spend Model

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.