Key points are not available for this paper at this time.
E. A. Cornish, R. A. Fisher, Moments and Cumulants in the Specification of Distributions, Revue de l'Institut International de Statistique / Review of the International Statistical Institute, Vol. 5, No. 4 (Jan., 1938), pp. 307-320
Cornish et al. (Sat,) studied this question.