# In statistical terminology, what is the opposite of “peak”?

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?

• I've also heard trough. – Christoph Hanck Jul 28 '15 at 6:06
• 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. – TPArrow Jul 28 '15 at 9:06
• Basically it just like a function and then you have one minima. – RockTheStar Jul 28 '15 at 16:50

## 3 Answers

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.

• 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. – whuber Sep 20 '19 at 14:46

“Trough” is commonly used, although perhaps somewhat colloquial.

• I say "trough" all the time, but I've never thought of it as particularly informal. – Matt Krause Aug 22 '16 at 12:53

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"

• 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. – jjet Aug 1 '18 at 14:41