Στατιστική ανάλυση σεισμικών δεδομένων με τη χρήση της θεωρίας ακραίων τιμών
The main target of this dissertation is to present and apply several statistical methods from Extreme Value Theory for the analysis of seismic data collected in the last decades from the broader area of Greece. Initially, we present the two main methods for studying and analyzing extremes, namely the Block Maxima and Peaks Over Threshold (POT) methods. According to the first method, the block maxima will approximately follow a Generalized Extreme Value (GEV) distribution. We use two methods for the estimation of the parameters of a GEV distribution that can also be applied to censored seismic samples: the method of Maximum Likelihood Estimation (MLE) and the method of Partial Probability Weighted Moments (PPWM). We also discuss the case when the block maxima asymptotically follow Gumbel’s third type (GIII or reversed Weibull) distribution, which can be considered as a special case of the GEV distribution. This distribution has been used by many authors for modeling seismic data. We empirically study the behavior of the MLE’s of GIII parameters when, in addition, we have a censored sample. Two data sets are being used for the application of the theory. The first set contains earthquakes which occurred in Greece in the period 1970-2007 (62053 observations) and the second set contains earthquakes which occurred in Greece in the period 1901-1996 (5991 observations).