The quadratic log frequency versus magnitude relationship is introduced into analytical engineering seismic risk analysis. The analytical risk relationships remain in closed form, and risk analysis remains easily amenable to computer implementation. The availability of both a quadratic relationship and a truncation point or upper bound on the magnitude (or epicentral intensity) permits relatively detailed representation of the large magnitude-low frequency region of the distribution. This region has an important influence on high intensity-low risk site conditions, which are of frequent engineering interest. At lower site intensities, the influence of the quadratic versus a linear form is apparently not significant.