Is a Cubed Normally Distributed Variable Still Normal?

[Jellis78]

Hi everybody,

I'm wrestling with the following problem:

Suppose a variable is normaly distributed, then is this same variable still normal distributed when raised to the power of 3? I know if the variable is raised to the power of 2 a chi-squared distribution is obtained, but what happens when raised to the power of 3?

I have a feeling that the variable is still normaly distributed but I can't prove it. Let me take this question one bit further; does anyone know what kind of transformation I have to apply to obtain the standard deviation of the transformed varaible?

Thank you and nice weekend

Jellis

 

[HallsofIvy]

The answer to your first question is, in general no. Any non-linear transformation of a normally distributed variable gives one that is not linearly distributed. I'm not sure why you would accept that the square of a normally distributed variable is not normally distributed but think that the cube would be!
How you would obtain the standard deviation of a transformed variable depends strongly on the transformation.

 

[Jellis78]

Hi,

Thanks for the reply.

Of course, If the chi-square distribution is not normal then the cubic isn't normaly distributed either.

I made a excel sheet in which I made the mistake to raise the 3rd power of the frequency instead of the variable of the distribution... No wonder it still looked normally distributed

I still meant the transformation of raising the 3rd power of a normal distributed variable. So let me rephrase th equestion:

What kind of mathematical operation do I need to do to obtain the standard deviation of this ‘new’ variable?

Hope you can link me some sort of solution on the web...

Jellis