@article{epos1548,
          volume = {31},
          number = {2},
          author = {Andrzej Kijko},
           title = {A modified form of the first Gumbel distribution: model for the occurrence of large earthquakes. Part II - Estimation of parameters},
       publisher = {Polish Academy of Science},
         journal = {Acta Geophysica Polonica},
           pages = {147--159},
            year = {1983},
             url = {https://episodesplatform.eu/eprints/1548/},
        abstract = {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[-{\ensuremath{\lambda}}((A2-A(x))/(A2-A1))] for Mmin{\ensuremath{<}}=x{\ensuremath{<}}=Mmax and G(x)=1 for x{\ensuremath{>}}Mmax, where A(x)=exp (-{\ensuremath{\beta}}x), A1=exp(-{\ensuremath{\beta}}Mmin), and A2=exp(-{\ensuremath{\beta}}Mmax). Mmin is the treshold magnitude, Mmax is the maximum regional value, and the parameters {\ensuremath{\beta}}, {\ensuremath{\lambda}} and Mmax have been determined. In this paper the formulas for the parameters {\ensuremath{\beta}}, {\ensuremath{\lambda}} 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.}
}