Distribution of the kth powers of normal random variables.

Question

If $X_1,..,X_n$ are standard normal random variables then it is known that:

1. $\sum_\limits{i=1}^n X_i$ is a normal random variable and
2. $\sum_\limits{i=1}^n X_i^2$ is a $\chi^2$-random variable.

My question is: is there a name for a random variable who of the form: $\sum_\limits{i=1}^n X_i^k$ for $k\geq 1$ (say $k$ is an integer)?