%0 Journal Article
%@ 1895-6572
%A Kijko, Andrzej
%A Institute of Geophysics, Polish Academy of Sciences, 00-973 Warsaw, P. O. Box 155, Pasteura 3,
%D 1983
%F epos:1548
%I Polish Academy of Science
%J Acta Geophysica Polonica
%N 2
%P 147-159
%T A modified form of the first Gumbel distribution: model for the occurrence of large earthquakes. Part II - Estimation of parameters
%U https://episodesplatform.eu/eprints/1548/
%V 31
%X In the first part of this paper (Kijko, 1982), the following cumulative distribution function for magnitudes of the largest earthquakes in a certain interval of time, was proposed: G(x)=exp[-λ((A2-A(x))/(A2-A1))] for Mmin<=x<=Mmax and G(x)=1 for x>Mmax, where A(x)=exp (-βx), A1=exp(-βMmin), and A2=exp(-βMmax). Mmin is the treshold magnitude, Mmax is the maximum regional value, and the parameters β, λ and Mmax have been determined. In this paper the formulas for the parameters β, λ and Mmax are derived following the maximum likelihood and moments principles. As an example, the proposed distribution and formulas are applied to five seismic regions.