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 $\alpha > 4$.
Publié le : 1988-04-14
Classification:
Determinate and indeterminate distributions,
normal distribution,
powers of a normal distribution,
60E05,
44A60
@article{1176991795,
author = {Berg, Christian},
title = {The Cube of a Normal Distribution is Indeterminate},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 910-913},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991795}
}
Berg, Christian. The Cube of a Normal Distribution is Indeterminate. Ann. Probab., Tome 16 (1988) no. 4, pp. 910-913. http://gdmltest.u-ga.fr/item/1176991795/