A derivation of conditional cumulants in exponential models

Abstract Let T = ( T 1,…, T k; k ≥ 2) be a minimal sufficient statistic for a k-parameter natural exponential model. Consider a partition of T into (T 1, T 2), where T 1 = ( T 1,…, T r) and T 2 = ( T r+1,…, T k; 1 < r ≤ k). It is shown that cumulants of the conditional distribution of T 1, given T 2 = t 2, can be computed through the marginal distribution of T 2 and the norming constant that makes the model a probability model. The results are illustrated by a few examples.