indicating that the mean rate for PGA > 0.05 g is equal to 0.075 per year, also very close to the total-probability calculation
(see Fig. 3). More importantly, the statistical test also supports that this larger seismic hazard should follow the Poisson
distribution as the test data shown in Fig. 9.
Fig. 10 shows the probability distribution for an even larger seismic hazard in PGA > 0.1 g. The MCS shows that the hazard
estimate is about 0.016 per year, also very close to 0.017 from the total-probability calculation (see Fig. 3). In addition, as
the comparison and statistical test data shown in Fig. 10, this seismic hazard in PGA > 0.1 g should be following the Poisson
distribution as well, with the support from MCS to statistical analysis.
5. Discussion: earthquake, seismic hazard, and the Poisson distribution
As mentioned previously, earthquake frequency following the Poisson distribution is commonly used in earthquake analyses,
including in this study. Nevertheless, it must be noted that the ‘‘earthquake-and-Poisson’’ relationship was supported
by earthquake observations in California or in Taiwan [21,22], making it more of a fact than an assumption.
By contrast, seismic hazard, which is a function of earthquake magnitude, distance, frequency, and ground motion models,
is a different random variable than earthquake. But without any tangible support in the literature, the ‘‘seismic-hazardand-Poisson’’
assumption has been an engineering judgment at best, until this study offering some evidence for the first
time from the novel application of Monte Carlo Simulation.
6. Summary
Seismic hazard is usually considered a variable following the Poisson distribution in earthquake studies. But without any
support in the literature, the key scope of this study is to evaluate this engineering assumption. The novelty of the study is
to apply Monte Carlo Simulation to solve the probabilistic analysis, instead of using total-probability algorithms currently
employed