Calculating Ratios of Moments: Spatial Extent of Distribution

[Jacob]

I've been told that there are useful interpretations of the ratios of moments of probability density distributions, such as <x^4>/<x^2>. I only have un-normalised values of the second and higher moments of the distribution of interest. Is there any way of quantifying the spatial extent of the distribution?

Thanks for any help.

 

[eddo]

I have limited knowledge of this, but since no one else is answering, I will offer what I have. Incase you don't already know, the first moment is the expectation, which can be interpreted as a sort of center of mass. The second central (about the mean/expectation) moment is the variance, which is analogous to the moment of inertia in physics. The variance is the square of the standard deviation, and is a measure of how "spread out" the distribution is.
The only other one i know of is the skew factor, which is the third central moment, divided by the second central moment (the variance) to the power of 3/2. (here only the denominator is raised to the power, not the third central moment). This is a measure of how symmetrical the distribuition is. Sorry that I can't help more.

 

[juvenal]

There's also kurtosis.

http://mathworld.wolfram.com/Kurtosis.html

What do you want to do exactly?

 

[Jacob]

Thanks for the help.

Unfortunately I only know unnormalised second and fourth moments of the distributions (which is why I need to divide the two!).

I have two similar distributions which I would like to compare on the basis of the unnormalised second and fourth moments.

 

[juvenal]

Well, one of the measures of kurtosis in that Mathworld link does use the unnormalized 4th and 2nd moments, so that should do the job.

 

[lorannex]

anyone can explain to me what is functionally complete gates ?