Modelling and Performance Comparison of Siesmic Data with Different Statistical Distributions

In this study, the performance of Nakagami distribution which is previously not used in the model of siesmic data is compared with known Generalized extreme value, Gumbel, Weibull distributions. The comparison criterion is the coefficient of determination and root mean square error. The siesmic magnitude data are analyzed separately and maximum siesmic magnitudes are obtained for each year and also block maxima (annual maximums) data set is determined. Considering the data obtained in the short periods with extreme value theory in the study, long-term probability of an earthquake has been obtained. Parameter estimations of the distributions fitted to the siesmic data and the variance-covariance matrices of these parameter estimates were determined. According to the coefficient of determination and root mean square error, it is determined that Nakagami distribution is also as successful as other known distributions in the modelling of siesmic data. On the other hand; the fitting to the observed siesmic data of the Gumbel distribution is revealed and return levels based on this distribution is estimated. Thus, the probability of having an earthquake of 5.1 is determined as 10% in the next 10 years