The coefficients in the General Hydrologic System (GHS) model of Chow and Kulandaiswamy (1971) are estimated using the method of cumulants. Based on this method a rational criterion is developed to determine the number of terms to be retained in the GHS Model. The least squares method used by Chow and Kulandaiswamy (1971) and the method of cumulants proposed here are compared and are found to yield comparable values of the model coefficients on an example watershed.