Probabilistic seismic hazard analysis (PSHA) is a regularly applied practice thatprecedes the construction of important engineering structures. The Cornell-McGuire procedure isthe most frequently applied method of PSHA. This paper examines the fundamental assumptionof the Cornell-McGuire procedure for PSHA, namely, the log-normal distribution of the residualsof the ground motion parameters. Although the assumption of log-normality is standard, it hasnot been rigorously tested. Moreover, the application of the unbounded log-normal distributionfor the calculation of the hazard curves results in non-zero probabilities of the exceedance ofphysically unrealistic amplitudes of ground motion parameters. In this study, the distribution ofthe residuals of the logarithm of peak ground acceleration is investigated, using the database ofthe Strong-motion Seismograph Networks of Japan and the ground motion prediction equationof Zhao and co-authors. The distribution of residuals is modelled by a number of probabilitydistributions, and the one parametric law that approximates the distribution most preciselyis chosen by the statistical criteria. The results of the analysis show that the most accurateapproximation is achieved with the generalized extreme value distribution for a central part of adistribution and the generalized Pareto distribution for its upper tail. The e ect of replacing alog-normal distribution in the main equation of the Cornell-McGuire method is demonstrated bythe calculation of hazard curves for a simple hypothetical example. These hazard curves di ersigni cantly from one another, especially at low annual exceedance probabilities.
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