Cumulant Generating Function

Definition

$K_X(t)=\ln M_X(t)=\ln E(e^{tX})$

Calculations of Cumulants

${\kappa }_n=K^{(n)}(0)$

the $n$-th cumulant can be calculated using cgf ${\kappa }_n=K^{(n)}(0)$