Estimation of Area under Receiver Operating Characteristic Curve for Bi-Pareto and Bi-Two Parameter Exponential Models


In this paper, we find the ROC curves for Bi-Pareto and Bi-two parameter exponential distributions. Theoretical, parametric and non-parametric values of area under receiver operating characteristic (AUROC) curve for different parametric combinations have been calculated using simulations. These values are compared in terms of root mean square and mean absolute errors. The results are demonstrated for two real data sets.

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B. Kaushal, K. Jain and S. Sharma, "Estimation of Area under Receiver Operating Characteristic Curve for Bi-Pareto and Bi-Two Parameter Exponential Models," Open Journal of Statistics, Vol. 4 No. 1, 2014, pp. 1-10. doi: 10.4236/ojs.2014.41001.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] S. Satchell and W. Xia, “Parametrical Models of the ROC Curve: Applications to Credit Rating Model Validation,” Quantitative Finance Research Centre Research Paper 181, University of Technology, Sydney, 2006.
[2] W. J. Krzanowski and D. J. Hand, “ROC Curves for Continuous Data,” Taylor and Francis Group, New York, 2009.
[3] D. Bamber, “The Area above the Ordinal Dominance Graph and the Area below the Receiver Operating Characteristic Graph,” Journal of Mathematical Psychology, Vol. 12, No. 4, 1975, pp. 387-415.
[4] J. A. Hanley and B. J. McNeil, “The Meaning and Use of the Area under ROC Curve,” Radiology, Vol. 4, 1982, pp. 49-58.
[5] D. M. Green and J. A. Swets, “Signal Detection Theory and Psychophysics,” Wiley, New York, 1966.
[6] A. P. Bradley, “The Use of the Area under ROC Curve in the Evaluation of Machine Learning Algorithms,” Pattern Recognition, Vol. 30, No. 7, 1997, pp. 1145-1159.
[7] N. L. Johnson and S. Kotz, “Continuous Univariate Distributions,” Vol. 1, Wiley, New York, 1970.
[8] S. J. Mason and N. E. Graham, “Area Beneath Relative Operating Characteristic (ROC) and Relative Operating Levels (ROL) Curve: Statistical Significance and Interpretation,” Quarterly Journal of the Royal Meteorological Society, Vol. 128, No. 584, 2002, pp. 2145-2166.
[9] J. P. Klein and M. L. Moeschberger, “Survival Analysis Techniques for Censored and Truncated Data,” Springer-Verlag, New York, 2003.
[10] T. R. Freireich, E. Gehan, E. Frei, L. R. Schroeder, I. J.Wolman, R. Anbari, E. O. Burgert, S. D. Mills, D. Pinkel, O. S. Selawry, J. H. Moon, B. R. Gendel, C. L. Spurr, R. Storrs, F. Haurani, B. Hoogstraten and S. Lee, “The Effect of 6-Mercaptopurine on the Duration of Steroid Induced Remissions in Acute Leukemia: A Model for Evaluation of Other Potentially Useful Therapy,” Blood, Vol. 21, No. 6, 1963, pp. 699-716.

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