改进用户流失预测模型，提升在波动购买行为场景下的稳定性与实用性。
A Simplified and Numerically Stable Approach to the BG/NBD Churn Prediction model
- 以连续M天无购买定义流失，更贴合实际业务场景。
- 简化公式并引入数值稳定技术，避免计算溢出或下溢。
- 适合电商、订阅服务等高频波动购买行业的流失预警应用。
本研究扩展了BG/NBD流失概率模型，针对受季节性事件影响明显且可能有高购买频率的行业中的客户行为问题。我们提出新的流失定义：若客户在连续M天内未发生任何购买，则视为已流失。贡献在于：第一，针对连续M天无购买的特定情况，简化了通用公式；第二，通过数值技术推导出替代表达式，有效缓解数值溢出或下溢问题。该方法为具有不规则购买模式的行业提供了更实用、更稳健的客户流失预测方案。
原文摘要 · Abstract (English)
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.
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