This should be a very easy answer for those who know the distribution. Lately, I am dealing a lot with the following distribution:


$\rho\left(x|u,s,p\right)=\frac{x^{pu-1}p}{s^{u}\Gamma\left(u\right)}\exp\left(-\frac{x^{p}}{s}\right)$


It is obtained by raising a gamma distributed random variable with shape $u$ and scale $s$ to the power $\frac{1}{p}$ ($p>0$). The resulting distribution is a generalization of the $\chi$-distribution (for $p=2$ and $u=\frac{n}{p}$) or, for arbitrary $p>0$, the generalization of the radial distribution of a multivariate $p$-generalized Normal (for $u=\frac{n}{p}$). 


My question is: Is there an "official" name for that distribution? 



name for the distribution of a gamma RV raise to 1/p?
I found the answer. It is embarrassingly simple: The distribution is called [Generalized Gamma Distribution](https://secure.wikimedia.org/wikipedia/en/wiki/Generalized_gamma_distribution%20%22Generalized%20Gamma%20Distribution%22). Who would have thought of that? The corresponding publication is:


Stacy EW. A Generalization of the Gamma Distribution. The Annals of Mathematical Statistics. 1962;33(3):pp. 1187-1192. Available at: <http://www.jstor.org/stable/2237889>.


