Some validations of and extensions to the Parametric‐Historic procedure as developed in a
two‐paper sequel by Andrzej Kijko and Gerhard Graham in 1998 and 1999 are presented.
The source‐free distribution they derive is validated through a somewhat more rigorous
mathematical derivation. The approach is also extended in two ways. The first extension
involves direct application of the estimators, which they used to determine maximum
regional magnitude, now to directly determine the maximum possible peak ground
acceleration at a specific site. The second extension is a generalization of the distribution of
peak ground acceleration in a semi‐closed form solution to incorporate a wider range of
ground motion prediction equations. The first extension is straightforward and is
simultaneously developed and validated by example application to actual ground motion
data. The second extension is derived and then applied to a specific ground motion
prediction equation as example to illustrate its performance.