 The nth cumulant is the nth derivative of the cumulant generating function with respect to "t" evaluated at "t" = 0.The cumulant generating function is
The first cumulant is 
The mean is the first moment and always equal to the first cumulant, so 

The variance is always the second cumulant, and it is always related to the first and second moments by 
so that

Likewise, the "n"th cumulant is 

2.Natural exponential families (NEF) are closed under convolution.