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Let $f:\mathbb{R}\rightarrow \mathbb{R}$. Let $f_{\mathrm{max}}=\max_{x\in \mathbb R} f(x)$ and $f_{\mathrm{min}}=\min_{x\in \mathbb R} f(x)$. Define $r$ as the ratio of $f_{\mathrm{max}}$ to $f_{\mathrm{min}}$.

Intuitively, $r$ measures the "turbulence" of $f$. Is there a specific terminology for $r$?

  • if you want to measure spread, would not https://en.wikipedia.org/wiki/Standard_deviation be a better measure ? – MBobrik Feb 29 '24 at 12:10
  • @MBobrik I have to use the exact definition of $r$ in my work, so I was wondering whether this ratio has been named. – Mengfan Ma Mar 01 '24 at 10:26

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