Brands share more of their customers with bigger competitors and fewer with smaller ones. However, there are occasional deviations to this predictable Duplication of Purchase (DoP) pattern. When two or more brands share excess customers because of functional or nonfunctional differences—it is called a partition. While past research using the NBD-Dirichlet model demonstrates partitions in annual or shorter data, there is no empirical evidence for partition persistency over the longer term, although some other NBD-Dirichlet deviations are known to persist over time. Examining expected partitions in 10 consumer goods categories in the United Kingdom, the authors show partitions overwhelmingly persist over 3 years. The findings contribute support to Dirichlet theory, especially on market stability, boundary conditions, and provide practical implications for portfolio management.

中文翻译：

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购买分区的重复性有多持久？

品牌与更大的竞争对手分享更多的客户，而与较小的竞争对手分享更少的客户。但是，这种可预测的重复购买 (DoP) 模式偶尔会出现偏差。当两个或多个品牌由于功能或非功能差异而共享过多的客户时，称为分区。虽然过去使用 NBD-Dirichlet 模型的研究证明了年度或更短数据中的分区，但没有经验证据表明分区在长期内具有持久性，尽管已知其他一些 NBD-Dirichlet 偏差会随着时间的推移而持续存在。作者检查了英国 10 个消费品类别的预期分区，结果显示分区绝大多数会持续 3 年以上。这些发现有助于支持狄利克雷理论，特别是在市场稳定性、边界条件、