We performed a comprehensive statistical analysis over six functional expressions of frequency–magnitude distributions (FMDs). We tested the goodness of fit on the basis of the Kolmogorov–Smirnov criterion, and performed a model selection using the Akaike information criterion over 15,000 subcatalogs spanning different sizes and covering different areas of the world. Results showed that the FMD proposed by Ogata and Katsura (1993) usually performs better than the others even if, in general, it would be appropriate to check the goodness of fit and do a model selection using statistical tools.

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