## The Annals of Probability

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

### The Cube of a Normal Distribution is Indeterminate

#### 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