Bivariate ROC Curve

이변량 ROC곡선

  • Hong, C.S. (Department of Statistics, Sungkyunkwan University) ;
  • Kim, G.C. (Research Institute of Applied Statistics, Sungkyunkwan University) ;
  • Jeong, J.A. (Research Institute of Applied Statistics, Sungkyunkwan University)
  • 홍종선 (성균관대학교 통계학과) ;
  • 김강천 (성균관대학교 응용통계연구소) ;
  • 정진아 (성균관대학교 응용통계연구소)
  • Received : 2011.11.08
  • Accepted : 2012.02.27
  • Published : 2012.03.31


For credit assessment models, the ROC curves evaluate the classification performance using two univariate cumulative distribution functions of the false positive rate and true positive rate. In this paper, it is extended to two bivariate normal distribution functions of default and non-default borrowers; in addition, the bivariate ROC curves are proposed to represent the joint cumulative distribution functions by making use of the linear function that passes though the mean vectors of two score random variables. We explore the classification performance based on these ROC curves obtained from various bivariate normal distributions, and analyze with the corresponding AUROC. The optimal threshold could be derived from the bivariate ROC curve using many well known classification criteria and it is possible to establish an optimal cut-off criteria of bivariate mixture distribution functions.


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