Volume-weighted average/moment of a probability distribution function

Hello,

I would like to calculate the volume-weighted mean of an obtained fitted weibull distribution.
For this, I thought about using the "third moment" of this distribution function and I want to make sure that the definition "3rd moment" corresponds to the I read a volume weighted average. The k-th moment, is defined as (with F(x) being the distribution function

http://upload.wikimedia.org/wikipedi...0d5908b918.png http://upload.wikimedia.org/wikipedi...0d5908b918.png

and since my volume weighted mean corresponds to x³ this should be (in my opinion) the 3rd moment.

Am I completely wrong?

In this case, could anyone tell me how to get the volume weighted average of a Weibull distribution?

Thanks a lot!!! (Happy)