Next, by ‘‘counting’’ the 10,000 data in Fig. 7, we developed the hazard’s probability function as shown in Fig. 8. In addition,
given the mean rate (i.e., the model parameter of the Poisson distribution) calculated as 1.022, we also show the theoretical
Poisson distribution in Fig. 8 for the comparison. Excitingly, the two are in a very good agreement from the analyses.
As many other studies [21,22], we further performed Chi-square tests to examine the model’s goodness-of-fit in a more
quantitative manner. (Details of the statistical test are given in the Appendix.) Accordingly, the Chi-square value (χ
2
) of the
test data is equal to 6.95, lower than the critical value of 11.07 given a 5% level of significance employed by the test. Therefore,
with the tangible, quantitative support from MCS to statistical analysis, this study offers some evidence for the first time that
seismic hazard should follow the Poisson distribution as the relationship has been commonly used in earthquake studies