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.

翻译：本研究对BG/NBD客户流失概率模型进行了扩展，以解决其在客户行为常受季节性事件影响且购买次数可能较高的行业中的局限性。我们提出了一种改进的流失定义：若客户在M天内未进行任何购买，则视为已流失。我们的贡献主要有两方面：首先，针对M天内零购买这一特定情况，我们简化了通用方程。其次，我们利用数值技术推导了一种替代表达式，以缓解数值上溢或下溢问题。该方法为购买模式不规则的行业提供了一种更实用、更稳健的客户流失预测方法。