Quantifying concordance between two random variables is crucial in applications. Traditional estimation techniques for commonly used concordance measures, such as Gini's gamma or Spearman's rho, often fail when data contain ties. This is particularly problematic for zero-inflated data, characterized by a combination of discrete mass in zero and a continuous component, which frequently appear in insurance, weather forecasting, and biomedical applications. This study provides a new formulation of Gini's gamma and Spearman's footrule, two rank-based concordance measures that incorporate absolute rank differences, tailored to zero-inflated continuous distributions. Along the way, we correct an expression of Spearman's rho for zero-inflated data previously presented in the literature. The best-possible upper and lower bounds for these measures in zero-inflated continuous settings are established, making the estimators useful and interpretable in practice. We pair our theoretical results with simulations and two real-life applications in insurance and weather forecasting, respectively. Our results illustrate the impact of zero inflation on dependence estimation, emphasizing the benefits of appropriately adjusted zero-inflated measures.

翻译：量化两个随机变量之间的一致性在应用中至关重要。对于常用的Gini's gamma或Spearman's rho等一致性度量，传统估计方法在数据存在结时往往失效。这在零膨胀数据中尤为突出——这类数据同时具有零点处的离散集中和连续分量特征，常见于保险、天气预报和生物医学应用。本研究针对零膨胀连续分布，提出了两种基于秩且包含绝对秩差的一致性度量（Gini's gamma与Spearman's footrule）的新表述形式。研究过程中，我们修正了文献中先前提出的零膨胀数据Spearman's rho表达式。建立了这些度量在零膨胀连续设定下可能达到的最优上下界，使估计量在实践中兼具实用性和可解释性。我们将理论结果与模拟实验及两个实际应用（分别来自保险和天气预报领域）相结合进行验证。研究结果揭示了零膨胀现象对依赖性估计的影响，并凸显了经适当调整的零膨胀度量方法的优势。