Exponential law with both positive and negative values

Question

The exponential law with density $f(x) = \lambda e^{-\lambda x}$ for $x \geq 0$ and $f(x)=0$ for $x < 0$, is well-known.

What's the name of the distribution which has

$$f(x) = \frac{1}{2} e^{-|x|} \qquad (x \in \mathbb R)$$

as a density?

Here the density of this distribution in green, and the density of a normal distrubtion in red:

Answer 1

This is sometimes called the Laplace distribution. See this article. I think I've also seen it called the "bilateral exponential distribution". Sometimes it is called the "double exponential distribution", although that term is also used for the Gumbel distribution, whose cumulative distribution function is $x\mapsto e^{-e^{-x}}$.