I'm looking for a simplified table that shows how to compute the cumulant cum(x1, x2, ... xn) for multiple variables, n > 4.
I know that the 2nd and 3rd order cumulants are equivalent to the compound moments of the same order. For the 4th order cumulant one also has to include the partitions such that after simplification one gets: cum(x1,x2,x3,x4) = E{x1,x2,x3,x4} - E{x1,x2}E{x3,x4} - E{x1,x3} * E{x2,x4} - E{x1,x4} * E{x2,x3} according to: http://sipi.usc.edu/~mendel/publications/HOSATutorial.pdf (This source also shows how you can generically get the cumulant for higher orders (p.297) but just applying this term would result in very long terms, making it infeasible to use it in real computations). I am hoping that such a table already exists somewhere, given that there are also other people who do work with higher order cumulants.
