Balancing Tails when Comparing Distributions: Comprehensive Equity Index (CEI) with Application to Bias Evaluation in Operational Face Biometrics

• A new metric is proposed to compare statistical distributions, with a focus on detecting disparities in the distribution tails. • The method separately analyzes genuine and impostor score distributions to provide a view of bias in high-performance biometric systems. • The proposal was tested extensively on real-world, and large-scale operational scenarios. Demographic bias in high-performance face recognition (FR) systems often eludes detection by existing metrics, especially with respect to subtle disparities in the tails of the score distribution. We introduce the Comprehensive Equity Index (CEI), a novel metric designed to address this limitation. CEI uniquely analyzes genuine and impostor score distributions separately, enabling a configurable focus on tail probabilities while also considering overall distribution shapes. Our extensive experiments (evaluating state-of-the-art FR systems, intentionally biased models, and diverse datasets) confirm CEI’s superior ability to detect nuanced biases where previous methods fall short. Furthermore, we present CEI A , an automated version of the metric that enhances objectivity and simplifies practical application. CEI provides a robust and sensitive tool for operational FR fairness assessment. The proposed methods have been developed particularly for bias evaluation in face biometrics but, in general, they are applicable for comparing statistical distributions in any problem where one is interested in analyzing the distribution tails.