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The joint cumulant of several random variables X1, ..., Xn is

where π runs through the list of all partitions of { 1, ..., n }, and B runs through the list of all block of the partition π.  For example,

The joint cumulant of just one random variable is its expected value, and that of two random variables is their kovarian.  If some of the random variables are idependent of all of the others, then the joint cumulant is zero.  If all n random variables are the same, then the joint cumulant is the nth ordinary cumulant.

The combinatorial méaning of the expression of moments in terms of cumulants is éasier to understand than that of cumulants in terms of moments:

where κ(XB) is the joint cumulant of those among the random variables  X1, ..., Xn whose indices are included in the block B.  For example: