## Cumulant-Generating Function

Let be the Moment-Generating Function. Then

If

is a function of independent variables, the cumulant generating function for is then

Kenney, J. F. and Keeping, E. S. Cumulants and the Cumulant-Generating Function'' and Additive Property of Cumulants.'' §4.10-4.11 in Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, pp. 77-80, 1951.