The Population Stability Index (PSI) is a widely used measure in credit risk modeling and monitoring within the banking industry. Its purpose is to monitor for changes in the population underlying a model, such as a scorecard, to ensure that the current population closely resembles the one used during model development. If substantial differences between populations are detected, model reconstruction may be necessary. Despite its widespread use, the origins and properties of the PSI are not well documented. Previous literature has suggested using arbitrary constants as a rule-of-thumb to assess stability, regardless of sample size. However, this approach too often calls for model reconstruction in small sample sizes while not detecting the need often enough in large sample sizes. This paper introduces an alternative discrepancy measure called the Population Resemblance statistic (PRS). It is based on the Pearson chi-square statistic. Properties of the PRS follow from the non-central chi-square distribution. Notably, the PRS accommodates sample-size dependent critical values and enables the specification of risk tolerances. Its efficacy is demonstrated in a simulation study and with real-world examples.

翻译：群体稳定性指数（PSI）是银行业信用风险建模与监测中广泛使用的指标，其目的在于监测模型（如评分卡）所依托的群体变化，确保当前群体与模型开发阶段使用的群体高度相似。若检测到群体间存在显著差异，则可能需要对模型进行重建。尽管PSI应用广泛，但其起源与统计性质尚未得到充分论证。既往研究常采用任意常数作为经验法则来评估稳定性，而忽略样本量差异。然而，该方法在小样本情境下过于频繁地触发模型重建需求，在大样本情境下却难以有效识别风险。本文提出一种替代性差异测度——群体相似性统计量（PRS），该统计量基于皮尔逊卡方统计量构建，其性质源自非中心卡方分布。值得注意的是，PRS可生成依赖样本量的临界值，并支持风险容忍度的量化设定。通过模拟研究与实际案例验证，该方法的有效性得到充分证实。