For every positive integer $n$, $nx^{n-1}$ is a probability density function in $[0,1]$. What is it called?
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1$\begingroup$ stats.stackexchange.com/questions/18433/… $\endgroup$– Christoph HanckJan 18 '18 at 9:52
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$\begingroup$ Thanks. So it is a Beta distribution with $\alpha=n$ and $\beta=1$. $\endgroup$– user7669Jan 18 '18 at 10:39
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The distribution with pdf
$$ f(x) = \frac{\beta x^{\beta-1}}{\alpha^\beta} $$
is known as the "power distribution" (unfortunately, it’s a very google-unfriendly name). It is alternatively parametrized by $k = 1/\alpha$. It has the $(0, \alpha]$ support.
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$\begingroup$ I think the version here on $[0,1]$ is a "standard power function distribution" $\endgroup$– HenryJun 3 '20 at 9:52