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I recently submitted a statistical article to a psychological journal.
This article made use of various joint central moments of bivariate
distributions.  One of the reviewers expressed the opinion that while
many readers of that journal would know what a "Kodak moment" was,
very would have any intuitions about the joint central moments I was
using.  I've looked without success for names or intuitive explanations
for various joint central moments.  Can anyone on the net help?

More specifically, here is the problem.  For a bivariate distribution
of X and Z, we can define joint central moments (using the notation of
Kendall & Stuart) as

   mu(j,k) = E[(X-Xmean)^j (Z-Zmean)^k]

So mu(2,0) and mu(0,2) are the univariate variances and intuitive
explanations are available.  Further, mu(3,0) represents skewness and
mu(4,0) reflects kurtosis.  For the bivariate, mu(1,1) is the
covariance and it is fairly easy to explain that to the "Kodak moment"
folks.  However, I'm really in need of names and/or explanations for
mu(2,1), mu(1,2), and mu(2,2).  Help please!

mu(2,1) and mu(1,2) are related to skewness because one can show that
if the conditional univariate distributions are symmetric then mu(2,1)
= mu(1,2) = 0.  But does anyone have a name for mu(2,1) or any other
insights about what it tells us about the joint distribution?

I've informally in my own notes been calling mu(2,2) the "double
variance" because when X and Z are stochastically independent, mu(2,2)
equals the product of the respective univariate variances.  Anyone have a
better name or insights about what mu(2,2) tells us?

Any suggestions or references would be greatly appreciated.  I'll
summarize any direct email replies in a subsequent post.

thanks for any help!

gary mcclelland
univ of colorado
mcclella@yertle.colorado.edu