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What are the possible shapes of an ROC curve? Is it necessary for an ROC curve to be shaped like a normal distribution curve?

Can we regard the following two curves as ROC with the area under the curve equal to 0.925 and 0.950, respectively?

ROC with 0.925 area under curve

ROC with 0.925 area under curve

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    $\begingroup$ You might state your ultimate goal, and how ROC curves provide insights (if they do) towards meeting that goal. $\endgroup$ – Frank Harrell Mar 30 '15 at 18:33
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Valid ROC curves must be monotonically increasing, start at $(0,0)$ and arrive at $(1,1)$, that's about it. Both shown curves are valid.

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