Description: In calculations involving the distribution of total claims in a risk theory setting, several authors have found it desirable to approximate a risk-theoretic distribution by use of the incomplete gamma function. A recent paper evaluated an excess loss ratio premium by use of a gamma distribution whose first and second moments agreed with those of the risk-theoretic loss distribution. A discussion of that paper pointed out that a translated gamma distribution allowed one to make the approximate distribution agree with the risk-theoretic distribution as far as the first three moments are concerned. The method presented in this paper allows one to make as many moments of the approximate distribution as desired agree with those of the risk-theoretic loss distribution. From Transactions of Society of Actuaries 1966, Vol. 18, Pt. 1, No. 52.