The cumulants of a distribution are formed by specific combinations of the moments. Knowledge of a distribution’s cumulants is equivilent to knowledge of its moments, in the sense that each can be computed from the other.
The symbol kappa is usually used to indicte a cumulant.
In some applications it is more convenient to use cumulants than moments. For example, there is a simple formula for the nth cumulants of the binomial distribution, but no simple formula for its nth moment.
When two distributions are convolved, their cumulants simply add.
Cumulants are also refered to as semi-invariants.