방법 비교

	BG/NBD Model	Pareto/NBD Model
분야	마케팅	마케팅
계열	Regression model	Regression model
기원 연도	2005	1987
창시자	Peter S. Fader, Bruce G. S. Hardie & Ka Lok Lee	David C. Schmittlein, Donald G. Morrison & Richard Colombo
유형	Probabilistic buy-till-you-die model of repeat transactions	Probabilistic buy-till-you-die model with continuous-time dropout
원전	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.	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.
별칭	Beta-Geometric/NBD Model, BG/NBD, Buy-Till-You-Die Model, Fader-Hardie-Lee Model	Pareto/NBD, Schmittlein-Morrison-Colombo Model, Counting Your Customers Model, SMC Model
관련	4	4
요약	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.	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.