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ROC curves are monotonically increasing functions $[0, 1] \rightarrow [0, 1]$ which start in (0, 0) and end in (1, 1). They are "over" the diagonal $x$.

They look a bit like $1/x$, but moved to the upper left and always above $x$.

Is there a parametrized form for such functions?

Background

I want to make a small explanation of those. This is what I have so far (code):

enter image description here

Martin Thoma
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    You can use $x^\alpha$ with $0\le \alpha \le 1$ – N74 Jun 24 '18 at 14:13
  • @N74 Nice! I think I would accept that as an answer. It would be even better if I could specify a point $(0, 1) \times (0, 1)$ through which the function went in a smooth way – Martin Thoma Jun 24 '18 at 19:24
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    As $y=x^\alpha$, $\alpha={\ln y_0 \over \ln x_0}$ where the point you want to pass through is $(x_0, y_0)$ – N74 Jun 24 '18 at 20:13
  • Nice! Should I make a community wiki answer or do you want to make an answer? – Martin Thoma Jun 24 '18 at 20:52
  • By the way, here is it on Wikipedia: https://commons.wikimedia.org/wiki/File:Roc-draft-xkcd-style.svg – Martin Thoma Jun 24 '18 at 20:53

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