Finitely Generated Cumulants
Giovanni Pistone, Henry P. Wynn · PORTO Publications Open Repository TOrino (Politecnico di Torino) · 1999
Computations with cumulants are becoming easier through the use of computer algebra but there remains a difficulty with the finiteness of the computations because all distributions except the normal have an infinite number of non-zero cumulants. One is led therefore to replacing finiteness of computations by “finitely generated” in the sense of recurrence relationships. In fact it turns out that there is a natural definition in terms of the exponential model which is that the first and second derivative of the cumulant generating function, K, lie on a polynomial variety. This generalises recent polynomial conditions on variance functions. This is satisfied by many examples and has applications to, for example, exact expressions for variance functions and saddle-point approximations.