The Annals of Probability

The Cube of a Normal Distribution is Indeterminate

Christian Berg

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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 $\alpha > 4$.

Article information

Source
Ann. Probab., Volume 16, Number 2 (1988), 910-913.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991795

Digital Object Identifier
doi:10.1214/aop/1176991795

Mathematical Reviews number (MathSciNet)
MR929086

Zentralblatt MATH identifier
0645.60018

JSTOR
links.jstor.org

Subjects
Primary: 60E05: Distributions: general theory
Secondary: 44A60: Moment problems

Keywords
Determinate and indeterminate distributions normal distribution powers of a normal distribution

Citation

Berg, Christian. The Cube of a Normal Distribution is Indeterminate. Ann. Probab. 16 (1988), no. 2, 910--913. doi:10.1214/aop/1176991795. https://projecteuclid.org/euclid.aop/1176991795


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