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Another Look at the Zero Integral Difference Between Lorenz and Concentration Curves in Supervised Learning

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  • Denuit, Michel

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Trufin, Julien

    (Université Libre de Bruxelles)

Abstract

We revisit the area between the concentration and Lorenz curves (ABC) criterion for model assessment in supervised learning. Insurance pricing is considered throughout the paper to illustrate the concepts but the results apply to any other setting where the mean of a response must be estimated from data. Building on the characterization of these curves, we provide new equivalent formulations for the case where the ABC vanishes. First, we characterize a vanishing ABC as the absence of correlation between pricing error and the ranks induced by the candidate premiums, making the link with Gini and Co-Gini coefficients. In both the discrete and continuous cases, we then show that a vanishing ABC corresponds to global balance in transformed portfolios that overweight either lower or higher premium classes. These results complement existing work on auto-calibration and contribute to a better understanding of ABC as a diagnostic tool in insurance pricing and related applications.

Suggested Citation

  • Denuit, Michel & Trufin, Julien, 2026. "Another Look at the Zero Integral Difference Between Lorenz and Concentration Curves in Supervised Learning," LIDAM Reprints ISBA 2026024, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2026024
    DOI: https://doi.org/10.1007/s11009-026-10282-x
    Note: In: Methodology and Computing in Applied Probability, 2026, vol. 28, 42
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