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In this study, the biased estimators for the shape parameter of classical Pareto distribution by using the maximum likelihood estimator and the unbiased estimator are proposed. Mean square errors of these biased estimators are smaller than mean square errors of maximum likelihood estimator and the unbiased estimator. Then the unbiased estimator and the maximum likelihood estimator are compared with obtained biased estimators by means of simulation study and conclusions are interpreted. [ABSTRACT FROM AUTHOR]

The goodness of fit of a statistical model tests how well it fits a set of observations. In this study, some goodness of fit tests called Kolmogorov- Smirnov, Anderson- Darling, Jarque Bera tests and also the tests given by Zhang(2002), Esteban et al.(2007) are investigated. In addition, a power comparison is made to determined which tests under what circumstances they are superior to the others. These test are compared under symmetrical and nonsymmetrical distributions over (-∞,∞) and (0, ∞). [ABSTRACT FROM AUTHOR]

In this study, calculation of the spatial distribution of seismicity parameters and seismic hazard is implemented for the Southeastern Anatolia Region of Turkey. For this purpose, the earthquakes of magnitude of M≥4 occurred in the time period between 1964-2008 were used in the Southeastern Anatolia Region of Turkey. For the estimation of seismicity parameters and its mapping, the study area is divided into 253 circular subregion. For each area, the parameters a and b in the Gutenberg-Richter magnitude-frequency relation were calculated by the least squares and the newly developed Kaltek method. The results obtained from the both methods were compared with each other. However, the b-value map prepared with the Kaltek method presented a better consistency with the regional tectonics. In the region, minimum, maximum and average b-value were calculated to be equal to bmin=0.8, bmax=l.26 and bavr=1, respectively. Finally, the return period and occurrence probability of M≥6,5 earthquake in the 100-year period were calculated using the Poisson distribution. An occurrence probability of 70-75% and a return period of less than 50 years were found for the Erzincan-Erzurum- Muş-Elaziğ area. [ABSTRACT FROM AUTHOR]