Multivariate probability distribution

[beman]

"In multivariate probability distribution higher-order cumulants contain information of decreasing significance, unlike higher-order moments".

 

[jedishrfu]

Can you provide more detail? is this for a course? did you read it in some book? what is the context of your question?

 

[statdad]

For normal distributions cumulants above those of second order vanish, which pretty much means they don't contribute much information.

 

[beman]

In multivariate probability distribution the first two cumulants are the means and covariances.Higher-order cumulants contain information of decreasing significance, unlike higher-order moments.We cannot set all moments higher than a certain order equal to zero since E(X^2n)>=E(X^n)^2 and thus,all moments contain information about
the lower moments.

 

[statdad]

In multivariate probability distribution the first two cumulants are the means and covariances.Higher-order cumulants contain information of decreasing significance, unlike higher-order moments.We cannot set all moments higher than a certain order equal to zero since E(X^2n)>=E(X^n)^2 and thus,all moments contain information about
the lower moments.

Again - for normal distributions, cumulants of order higher than two are zero: it isn't decreasing significance, it is no significance.