Abstract: In order to establish a probability distribution model of peak ground acceleration, 255,365 ground motion recordings were collected from 500 stations to create initial statistical samples of peak ground acceleration. The generalized extreme value distribution was employed as the probability model for peak ground acceleration. The effectiveness of the maximum likelihood estimation method and the linear moment estimation method, commonly used for estimating parameters of the extreme value distribution model, was assessed using the established generalized extreme value distribution model. Based on the asymptotic normality of the maximum likelihood estimation, a method was proposed to determine the minimum required sample length when establishing a generalized extreme value distribution model. The analysis indicated that, when constructing the generalized extreme value distribution model for peak ground acceleration in seismic events, the data sample size should not be less than 120. Statistical analysis was conducted on seismic peak ground acceleration data samples that met the sample size requirement. It was observed that the model parameters converged to a relatively narrow range as the sample size increased. Ultimately, probability statistical models for measured peak ground acceleration for different types of sites were established, along with seismic hazard calculation formulas.

Key words:  , generalized extreme value distribution, maximum likelihood estimation, minimum sample length, earthquake action probability distribution, seismic hazard