Gini Score Under Ties and Case Weights

The Gini score, a purely rank-based score that assesses risk rankings, is a popular tool for model validation and model selection in statistical modeling and machine learning. For statistical modeling, it has mainly been used in a binary context and has many equivalent reformulations such as the receiver operating characteristics curve or the area under the curve. In the actuarial literature, this rank-based score for binary responses has been extended to general real-valued random variables using the Lorenz curve, Leimkuhler curve, and concentration curve. While these initial concepts assume that the risk ranking is generated by a continuous distribution function, this paper discusses how the Gini score can be used in the case of ties in the risk ranking. Moreover, we adapt the Gini score to the common actuarial situation that includes case weights.