Extreme value distribution of earthquake magnitude

Probability distribution of maximum earthquake magnitude is first derived for an unspecified probability distribution of earthquake magnitude. A model for energy release of large earthquakes, similar to that of Adler-Lomnitz and Lomnitz, is introduced from which the probability distribution of earthquake magnitude is obtained. An extensive set of world data for shallow earthquakes, covering the period from 1904 to 1980, is used to determine the parameters of the probability distribution of maximum earthquake magnitude. Because of the special form of probability distribution of earthquake magnitude, a simple iterative scheme is devised to facilitate the estimation of these parameters by the method of least-squares. The agreement between the empirical and derived probability distributions of maximum earthquake magnitude is excellent.