Statistical characteristics of earthquake magnitude based on the composite model

Threshold selection is challenging when analyzing tail data with a generalized Pareto distribution. Data below the threshold was not used in the model, resulting in incomplete characterization of the whole data. This paper applied the Gamma distribution, Weibull distribution, and lognormal distribution to fit the central data separately, and a generalized Pareto distribution (GPD) was used to analyze the tail data. In such composite models, the thresholds are estimated directly as parameters. We proposed an empirical distribution function-based parameter estimation method. The absolute value of the difference between the empirical distribution function and the composite distribution function was used as a loss function to obtain an estimate of the parameter. This parameter estimation method is suitable for complex multiparameter distributions. The estimation method based on the empirical distribution function was verified to be feasible through simulation studies. The composite model and the estimation method based on the empirical distribution function were applied to study the earthquake magnitude data to provide a reference for earthquake hazard analysis.