مقایسهٔ روش‌ها

	Gamma-Gamma Spend Model	BG/NBD Model
حوزه	بازاریابی	بازاریابی
خانواده	Regression model	Regression model
سال پیدایش	2013	2005
پدیدآور	Peter S. Fader & Bruce G. S. Hardie	Peter S. Fader, Bruce G. S. Hardie & Ka Lok Lee
نوع	Probabilistic model of monetary value per transaction	Probabilistic buy-till-you-die model of repeat transactions
منبع بنیادین	Fader, P. S., & Hardie, B. G. S. (2013). The Gamma-Gamma Model of Monetary Value. Technical note, www.brucehardie.com/notes/025/.	Fader, P. S., Hardie, B. G. S., & Lee, K. L. (2005). "Counting Your Customers" the Easy Way: An Alternative to the Pareto/NBD Model. Marketing Science, 24(2), 275-284.
نام‌های دیگر	Gamma-Gamma Model, Gamma/Gamma Spend Model, Monetary Value Model, Average Transaction Value Model	Beta-Geometric/NBD Model, BG/NBD, Buy-Till-You-Die Model, Fader-Hardie-Lee Model
مرتبط	4	4
خلاصه	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.	The BG/NBD (Beta-Geometric/Negative Binomial Distribution) model is a probabilistic buy-till-you-die model that predicts how many times a customer will transact in the future and whether that customer is still active, using only their past purchase recency and frequency. Introduced by Peter Fader, Bruce Hardie and Ka Lok Lee in their 2005 Marketing Science paper "Counting Your Customers the Easy Way," it was designed as a far simpler alternative to the Pareto/NBD model of Schmittlein, Morrison and Colombo while delivering comparable forecasts. The model couples a Poisson purchasing process, whose rate varies across customers by a gamma distribution, with a geometric dropout process governed by a beta-distributed dropout probability. The key behavioral story is that customers buy at a steady individual rate while alive and become permanently inactive with some probability immediately after any purchase. Because the latent attrition is unobserved, the model infers each customer's probability of still being alive from how recently and how often they bought. Its estimation requires only the (x, t_x, T) summary per customer and can even be fit in a spreadsheet, which made customer-base analysis practical for ordinary analysts.