A nonextensive modification of the Gutenberg–Richter law: q-stretched exponential form

We study the cumulative distribution for the magnitude of earthquakes in the context of nonextensive statistical mechanics. A new modification of the Gutenberg–Richter (GR) law is introduced. We use seismic data sets which were recorded in two different regions, Iran and California, to compute the cumulative distribution of the magnitudes. The empirical data are fitted extremely well by our suggested expression for the modified GR law over the whole range of magnitudes.