Since the usual Gutenberg and Richter distribution of magnitudes does not give good fit to the observed data except in the middle of the range, it is proposed to find a new distribution of magnitudes starting from the two principles: (a) distribution of all magnitudes (initial distribution) has to be limited; and (b) distribution of the largest values (extremal distribution) has to be asymptotic extremal distribution for the given initial distribution. Since it is well established that the largest values of intensity and magnitude follow the so-called third asymptote, which is conveniently written in Jenkinson's form, the initial distribution which belongs to this extremal distribution is determined. A procedure for determining the parameters of the initial distribution is proposed. For the time being, better results are obtained from macroseismic intensities, since often the magnitudes are being determined from these intensities by means of the linear regression. As an example, the frequency distribution of the 100-yr series of intensity of Zagreb earthquakes is analyzed. It seems that this initial distribution, which turns out to be the generalized exponential distribution, gives good fit to the data.

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