• The Korean Journal of Applied Statistics
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• v.22 no.1
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• pp.29-39
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• 2009

Among others, ROC and CAP curves are used to explore the discriminatory power between the defaults and non-defaults, based on the distribution of the probability of default in credit rating works. ROC and CAP curves are plotted in terms of various ratios of the probability of default. Each point on ROC and CAP curves is calculated according to cutting points (scores) for classifying between defaults and non-defaults. In this paper, adjusted ROC and CAP curves are proposed by using functions of ratios of the probability of default. It is possible to recognize the score corresponding to a point oil these adjusted curves, and we can identify the best score to show the optimal discriminatory power. Moreover, we discuss the relationships between the best score obtained from the adjusted ROC and CAP curves and the score corresponding to Kolmogorov - Smirnov statistic to test the homogeneous distribution functions of the defaults and non-defaults.

• 전자공학회논문지 IE
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• v.46 no.3
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• pp.62-67
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• 2009

In this paper, ROC curves were designed by using Fuzzy Logic Systems. ROC curve is used for diagnostic evaluation and the person evaluating ROC curve is chosen as a first-level diagnostician. For rating diagnostic capability on ROC curve through learning, the chest X-ray image is used. The images used for making a diagnosis are X-ray film being both noise and signal. The result over diagnostic capability difference between the male and the female represented a man had better than a woman but that difference can be ignored.

• Communications for Statistical Applications and Methods
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• v.19 no.2
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• pp.277-286
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• 2012

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.

• The Korean Journal of Applied Statistics
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• v.33 no.5
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• pp.541-553
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• 2020

The receiver operating characteristic (ROC) curve is expressed as both sensitivity and specificity; in addition, some optimal thresholds using the ROC curve are also represented with both sensitivity and specificity. In addition to the sensitivity and specificity, the expected usefulness function is considered as disease prevalence and usefulness. In particular, partial the area under the ROC curve (AUC) on a certain range should be compared when the AUCs of the crossing ROC curves have similar values. In this study, partial AUCs representing high sensitivity and specificity are proposed by using sensitivity and specificity lines, respectively. Assume various distribution functions with ROC curves that are crossing and AUCs that have the same value. We propose a method to improve the discriminant power of the classification models while comparing the partial AUCs obtained using sensitivity and specificity lines.

• The Korean Journal of Applied Statistics
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• v.24 no.2
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• pp.269-278
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• 2011

There are many researches that have considered the distribution functions and appropriate covariates corresponding to the scores in order to improve the accuracy of a diagnostic test, including the ROC curve that is represented with the relations of the sensitivity and the specificity. The ROC analysis was used by the regression model including some covariates under the assumptions that its distribution function is known or estimable. In this work, we consider a general situation that both the distribution function and the elects of covariates are unknown. For the ROC analysis, the mixtures of normal distributions are used to estimate the distribution function fitted to the credit evaluation data that is consisted of the score random variable and two sub-populations of parameters. The AUC measure is explored to compare with the nonparametric and empirical ROC curve. We conclude that the method using normal mixtures is fitted to the classical one better than other methods.

• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.911-921
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• 2009

Receiver Operating Characteristic(ROC) and Cumulative Accuracy Profile(CAP) curves are two methods used to assess the discriminatory power of different credit-rating approaches. The points of optimal classification accuracy on an ROC curve and of maximal profit on a CAP curve can be found by using iso-performance tangent lines, which are based on the standard notion of accuracy. In this paper, we offer an alternative accuracy measure called the true rate. Using this rate, one can obtain alternative optimal threshold points on both ROC and CAP curves. For most real populations of borrowers, the number of the defaults is much less than that of the non-defaults, and in such cases the true rate may be more efficient than the accuracy rate in terms of cost functions. Moreover, it is shown that both alternative scores of optimal classification accuracy and maximal profit are the identical, and this single score coincides with the score corresponding to Kolmogorov-Smirnov statistic used to test the homogeneous distribution functions of the defaults and non-defaults.

• The Korean Journal of Applied Statistics
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• v.32 no.2
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• pp.187-198
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• 2019

Extensive literature exists on how to estimate optimal thresholds based on various accuracy measures using receiver operating characteristic (ROC) and cumulative accuracy profile (CAP) curves. This paper now proposes an alternative measure to represented the specific partial area under the ROC and CAP curves. The relationship between ROC and CAP functions is examined using differential equations of the new defined partial area under curves. In addition, the relationship with the optimal thresholds under conditions of various accuracy measures for the ROC and CAP functions is also derived. We assume there are two kinds of distribution functions composing the mixed distribution as various normal distributions before finding the optimal thresholds. Corresponding type 1 and 2 errors are also explored and discussed under various conditions for accuracy measures.

• The Korean Journal of Applied Statistics
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• v.24 no.1
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• pp.185-191
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• 2011

In the credit evaluation study with the assumption of mixture distributions, the ROC curve is a useful method to explore the discriminatory power of default and non-default borrowers. The AROC curve is an adjusted ROC curve that can be identified with the corresponding score and is mathematically analyzed in this work. We obtain patterns of this curve by applying normal distributions. Moreover, the relationship between the AROC curve and many classification accuracy statistics are explored to find the optimal threshold. In the case of equivalent variances of two distributions, we obtain that the local minimum of the AROC curve is estimated at the optimal threshold to maximize certain classification accuracies.

• Imaging Science in Dentistry
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• v.30 no.3
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• pp.155-158
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• 2000

The purpose of this paper is to explain the making procedure and the usage of receiver operating characteristic (ROC) curve for interpretation of radiographic images. The conventional radiograms obtained after the creation of the lesions in the acrylic plates and were enhanced in color. The observer were informed of which tooth to examine, the 'a priori' probability of a lesion present and the approximate diameter of the lesions. The two groups of films were interpreted separately by the same observer using the same rating scale. The following rating scale was used: A; definitely no lesion, B; probably no lesion, C; not sure, D; probably a lesion, and E; definitely a lesion. In analysis, for each observer the diagnostic results in terms of true positive (TP) and false positive (FP) decisions were plotted on a graph. The lowest point on the graph represents the TP and FP when only decisions designated as E according to the rating scale are included. The next point shows the TP and FP values when diagnoses designated as D are added and so forth. By connecting such plot points, a receiver operating characteristic (ROC) curves is obtained. The area under the curve represents the diagnostic accuracy resulting from a diagnostic performance at pure chance level and a value of 1.0 at perfect performance. This method has been known as an useful method to detect the minute difference for each radiographic technic, each observer and for the different lesion depths.

• The Korean Journal of Applied Statistics
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• v.35 no.1
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• pp.35-47
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• 2022

The receiver operating characteristic (ROC) curve was developed to quantify the classification ability of marker values (covariates) on the response variable and has been extended to survival data with diverse missing data structure. When survival data is understood as binary data (status of being alive or dead) at each time point, the ROC curve expressed at every time point results in time-dependent ROC curve and time-dependent area under curve (AUC). In particular, a follow-up study brings the change of cohort and incomplete data structures such as censoring and competing risk. In this paper, we review time-dependent ROC estimators under several contexts and perform simulation to check the performance of each estimators. We analyzed a dementia dataset to compare the prognostic power of markers.