ParetoNBD

The ParetoNBD model is a probabilistic, continuous-time model for predicting customer behavior. It is widely used in marketing analytics to estimate future purchases and customer lifetime value from transaction histories. The model jointly describes how many purchases a customer will make and how long the customer remains active before churn, treating purchase activity and attrition as stochastic processes.

In ParetoNBD, each customer has a personal purchase rate lambda drawn from a Gamma distribution across customers, and a dropout process with a Pareto-distributed lifetime. Conditional on these latent variables, purchases follow a Poisson process. Integrating over the Gamma priors yields a closed-form likelihood for observed data, enabling maximum-likelihood or Bayesian estimation of the four population-level parameters.

After fitting, the model provides the probability that a given customer is still active at a future horizon and the expected number of purchases in a future period. These forecasts support segmentation, customer lifetime value estimation, and budget planning based on predicted future cash flows.

ParetoNBD is related to the BG/NBD model (which uses a Beta-Geometric dropout). It is particularly suitable when lifetimes are long and heavy-tailed. Limitations include the assumption of time-stable rates, sensitivity to seasonality or promotions, and the need for sufficient transactional history to identify parameters.

Software implementations exist in analytics libraries such as BTYD (R) and related tools, facilitating fitting and forecasting without bespoke coding.