Abstract
It is established that if $X$ is a stochastic variable with a normal distribution, then $X^{2n+1}$ has an indeterminate distribution for $n \geq 1$. Furthermore, the distribution of $|X|^\alpha$ is determinate for $0 < \alpha \leq 4$ while indeterminate for $\alpha > 4$.
Citation
Christian Berg. "The Cube of a Normal Distribution is Indeterminate." Ann. Probab. 16 (2) 910 - 913, April, 1988. https://doi.org/10.1214/aop/1176991795
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