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When we see a curve (or a normal distribution), we describe the highest value as "peak".

Let's imagine we have a curve with only a minimum value (like an inverted hat), what do we call that minimum value?

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    $\begingroup$ I've also heard trough. $\endgroup$ Jul 28, 2015 at 6:06
  • $\begingroup$ what do you mean by curve? I guess curve is more mathematical that statistical. if you mean a mathematical concept it is called minima. I am interested in knowing a continues density function with just a minima. $\endgroup$
    – TPArrow
    Jul 28, 2015 at 9:06
  • $\begingroup$ Basically it just like a function and then you have one minima. $\endgroup$ Jul 28, 2015 at 16:50

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In signal processing, a commonly used term is negative peak. In mathematics, you use the terms vertex of parabola, highest or lowest point, maximum or minimum.

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  • $\begingroup$ This doesn't look like an accurate description of how mathematics understands parabolas. Indeed, it is rare indeed for any neighborhood of any local extremum of a density function to be part of a parabola, so the term "vertex of parabola" would almost never apply in this context. $\endgroup$
    – whuber
    Sep 20, 2019 at 14:46
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“Trough” is commonly used, although perhaps somewhat colloquial.

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    $\begingroup$ I say "trough" all the time, but I've never thought of it as particularly informal. $\endgroup$ Aug 22, 2016 at 12:53
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The peaks are called "local modes" (specifically, the x-value is called the mode, the height would be the density at the mode).

The highest one is sometimes called "the mode".

The bottoms of troughs are often called "antimodes"

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    $\begingroup$ It's worth noting that this term actually appears in statistical literature. It sounds a lot clunkier than "trough" though. Statisticians aren't always known to come up with clever terminology. $\endgroup$
    – jjet
    Aug 1, 2018 at 14:41

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