Does the function $f(x)=\log(-\log(x))$, $x\in(0,1)$ has a name? Equivalently, the function $g(y)=f^{-1}(y)=\exp(-\exp(y))$, $y\in{\mathbb R}$.
The only thing I want to know if whether this function is referred to with a particular name.
EDIT. The function $f$ is equivalent to the negative of the quantile Gumbel function (with location $0$ and scale $1$). Another user proposed to simply call it "Bob", the choice is yours.
The function $\log(-\log(x))$ is not in the standard canon of mathematical functions studied by most mathematicians. As far as I know, there is no name given to this function. If there is a name, then it is certainly not well known. The same is true for the exponential analogue of this function.
I hence declare this function's name to be Bob.