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Lorenz curve, Gini coefficient, and Tweedie dominance for autocalibrated predictors

Author

Listed:
  • Denuit, Michel

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

  • Trufin, Julien

    (Université Libre de Bruxelles)

Abstract

Denuit et al. (2019, 2021a, 2021b) proposed diagnostic tools based on concentration curves and associated metrics (ICC and ABC), as well as Tweedie dominance to compare competing models. This is in contrast with professional practice which generally resorts to Lorenz curves and Gini coefficients for that purpose. This note reconciles both approaches for autocalibrated predictors. Autocalibration is a desirable property, intimately related to the method of marginal totals that predates modern risk classification methods. It can easily be implemented using the practical method proposed by Denuit et al. (2021a), consisting in an extra local regression step. Under autocalibration, it is shown that Lorenz curve and concentration curve coincide, that ICC is equivalent to Gini coefficient, and that ABC is zero. The latter property thus offers an easy check for autocalibration.

Suggested Citation

  • Denuit, Michel & Trufin, Julien, 2021. "Lorenz curve, Gini coefficient, and Tweedie dominance for autocalibrated predictors," LIDAM Discussion Papers ISBA 2021036, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2021036
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    References listed on IDEAS

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    1. Denuit, Michel & Sznajder, Dominik & Trufin, Julien, 2019. "Model selection based on Lorenz and concentration curves, Gini indices and convex order," LIDAM Reprints ISBA 2019046, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Denuit, Michel & Sznajder, Dominik & Trufin, Julien, 2019. "Model selection based on Lorenz and concentration curves, Gini indices and convex order," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 128-139.
    3. Denuit, Michel & Sznajder, Dominik & Trufin, Julien, 2019. "Model selection based on Lorenz and concentration curves, Gini indices and convex order," LIDAM Discussion Papers ISBA 2019006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    Cited by:

    1. Denuit, Michel & Trufin, Julien, 2022. "Model selection with Pearson’s correlation, concentration and Lorenz curves under autocalibration," LIDAM Discussion Papers ISBA 2022033, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Denuit, Michel & Trufin, Julien, 2022. "Autocalibration by balance correction in nonlife insurance pricing," LIDAM Discussion Papers ISBA 2022041, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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