- Volume 20 Issue 3
The ROC curve is drawn with two conditional cumulative distribution functions (or survival functions) of the univariate random variable. In this work, we consider joint cumulative distribution functions of k random variables, and suggest a ROC curve for multivariate random variables. With regard to the values on the line, which passes through two mean vectors of dichotomous states, a joint cumulative distribution function can be regarded as a function of the univariate variable. After this function is modified to satisfy the properties of the cumulative distribution function, a ROC curve might be derived; moreover, some illustrative examples are demonstrated.
- Gardner, I. A. and Greiner, M. (2006). Receiver operating characteristic curves and likelihood ratios: Improvements over traditional methods for the evaluation and application of veterinary clinical pathology tests, American Society for Veterinary Clinical Pathology, 35, 8-17. https://doi.org/10.1111/j.1939-165X.2006.tb00082.x
- Greiner, M., Pfeiffer, D. and Smith, R. D. (2000). Principles and practical application of the receiver-operating characteristic analysis for diagnostic tests, Preventive Veterinary Medicine, 45, 23-41. https://doi.org/10.1016/S0167-5877(00)00115-X
- Metz, C. E. (1978). Basic principles of ROC analysis, Seminars in Nuclear Medicine, 8, 283-298. https://doi.org/10.1016/S0001-2998(78)80014-2
- Tasche, D. (2006). Validation of internal rating systems and PD estimates, arXiv.org, eprint arXiv:physics/0606071.
- Zweig, M. H. and Campbell, G. (1993). Receiver operating characteristic(ROC) plots: A fundamental evaluation tool in clinical medicine, Clinical Chemistry, 39, 561-577.