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Does this distribution have a name:

$f(x) = yx^{y-1}$ for $0 < x<1$ and $y>0$?

It looks like an exponential distribution. Or is it a nameless distribution?

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Aside: When $y \in \mathbb N$, this is the density function of the maximum of a sample of size $y$ of iid $\mathcal U(0,1)$ random variables. – cardinal Apr 18 '12 at 0:17
This is a beta distribution with $\beta=1$: – Byron Schmuland Apr 18 '12 at 0:25

As Byron Schmuland says, this is a beta distribution with the second parameter $\beta=1$.

It is sometimes called a "standard power-function distribution".

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