A Simplified and Numerically Stable Approach to the BG/NBD Churn Prediction model

TL;DR

This paper enhances the BG/NBD churn model by simplifying its equations and introducing numerically stable techniques, improving robustness for industries with seasonal and irregular customer purchase behaviors.

Contribution

It offers a simplified equation for zero-purchase periods and a numerically stable method to prevent overflow, advancing churn prediction accuracy and practicality.

Findings

Simplified the BG/NBD model equations for zero-purchase scenarios

Developed a numerically stable computational approach

Improved robustness in industries with irregular purchase patterns

Abstract

This study extends the BG/NBD churn probability model, addressing its limitations in industries where customer behaviour is often influenced by seasonal events and possibly high purchase counts. We propose a modified definition of churn, considering a customer to have churned if they make no purchases within M days. Our contribution is twofold: First, we simplify the general equation for the specific case of zero purchases within M days. Second, we derive an alternative expression using numerical techniques to mitigate numerical overflow or underflow issues. This approach provides a more practical and robust method for predicting customer churn in industries with irregular purchase patterns.