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The compound Poisson process is considered to model the frequency and the magnitude of the earthquake occurrences concurrently. Nevertheless, there are many debates on whether climate change influences the frequency of the natural disasters. In this study, we propose a compound Poisson process with change-point (CPPCP) model to fit the data with two-phase pattern. The hierarchical Bayesian method is employed via assigning a common distribution for the unit-specific parameters. For comparison purpose, we also develop the maximum-likelihood method. The simulation study illustrates the applicability of our proposed model and the validity of the hierarchical Bayesian method. In the analysis of the earthquake data, CPPCP model outperforms the quadratic linear regression model and the hierarchical Bayesian method is superior to the maximum-likelihood method in terms of the model fitting and prediction.