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 resemblance (or "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, the Population Resemblance statistic (PRS), based on the Pearson chi-square statistic. Properties of the PRS follow from the non-central chi-square distribution. Specifically, the PRS allows for critical values that are configured according to sample size and the number of risk categories. Implementation relies on the specification of a set of parameters, enabling practitioners to calibrate the procedure with their risk tolerance and sensitivity to population shifts. The PRS is demonstrated to be universally competent in a simulation study and with real-world examples.

翻译：人口稳定性指数（PSI）是银行业信用风险建模与监控中广泛使用的度量指标，其目的在于监测模型（如评分卡）底层人口分布的变化，以确保当前人口与模型开发阶段所用人口高度相似。若检测到人口间存在显著差异，则可能需要进行模型重构。尽管PSI应用广泛，其起源与统计特性却缺乏充分文献记载。先前文献建议使用任意常数作为经验法则来评估相似性（或称“稳定性”），而未考虑样本量的影响。然而，这种方法在小样本场景下往往过度要求模型重构，而在大样本场景下又未能充分检测到重构需求。本文基于皮尔逊卡方统计量提出了一种替代性差异度量指标——人口相似性统计量（PRS）。PRS的性质源自非中心卡方分布，其关键特性在于能够根据样本量和风险类别数量配置临界值。具体实施依赖于一组参数的设定，使从业者可根据自身风险容忍度及对人口变化的敏感度校准流程。通过模拟研究和实际案例验证，PRS被证明具有普适有效性。