For every positive integer $n$, $nx^{n-1}$ is a probability density function in $[0,1]$. What is it called?
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1https://stats.stackexchange.com/questions/18433/how-do-you-calculate-the-probability-density-function-of-the-maximum-of-a-sample – Christoph Hanck Jan 18 '18 at 09:52
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Thanks. So it is a Beta distribution with $\alpha=n$ and $\beta=1$. – user7669 Jan 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.
Tim
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I think the version here on $[0,1]$ is a ["standard power function distribution"](https://en.wikipedia.org/wiki/Talk:Beta_distribution#The_name_of_a_special_case?) – Henry Jun 03 '20 at 09:52