# Ratios of moments

1. Apr 26, 2005

### 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.

2. Apr 27, 2005

### eddo

I have limited knowledge of this, but since noone 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.

3. Apr 27, 2005

### juvenal

4. Apr 27, 2005

### 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.

5. Apr 28, 2005

### 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.

6. May 7, 2005

### lorannex

anyone can explain to me what is functionally complete gates ?