Multivariate probability distribution

beman
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"In multivariate probability distribution higher-order cumulants contain information of decreasing significance, unlike higher-order moments".
 
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Can you provide more detail? is this for a course? did you read it in some book? what is the context of your question?
 
For normal distributions cumulants above those of second order vanish, which pretty much means they don't contribute much information.
 
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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.
 
beman said:
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.
 

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