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    The Earthquake Risk Analysis Based On Copula Models For Turkey
    (Yildiz Technical Univ, 2017) Kizilok Kara, Emel
    This study aims to explore the dependence structure between magnitude and frequency for Turkey earthquake data. In the literature, the Gutenberg Richter (GR) model based on lineer regression is often used to determine this dependence. The dependence structure is evaluated using copula models in this study. Copulas are useful statistical tool for modeling the dependence structure so it does not require assumptions such as linearity and normality. Therefore, as well as GR model, various copula functions are used to determine the magnitude-frequency relationship of earthquakes. An application is given to illustrate that the copulas can be used as alternatives to the GR model. The best copula models are selected by goodness of fit tests. Additionally, the probabilities of earthquake occurrence and the bivariate return periods are estimated for these selected copula models. It is seen that the probabilities of earthquakes occurrence for GR and copula models are almost identical, whereas the return periods based on copula models is more realistic than GR approach.
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    Modeling asymmetrically dependent automobile bodily injury claim data using Khoudraji Copulas
    (Yildiz Technical University, 2024) Kizilok Kara, Emel; Açik Kemaloğlu, Sibel
    Linear-dependent variables are typically modeled through the Spearman correlation, a classical statistical technique. In reality, the dependence between the data cannot always be linear. The copula approach has often been a popular tool for modeling dependent data in these cases. Archimedean copulas, which can model mostly symmetrical data, are also among the copula families used for this purpose. Recently, asymmetric copula models have been developed to model unsymmetrical-dependent variables. The dependency measure is calculated using directional dependency coefficients instead of the Spearman correlation when the data is asymmetrical. Appropriate asymmetric model selection is made with the help of these measurements. In the study, first, dependency parameters corresponding to different Spearman coefficients were obtained for Archimedean copula families, and asymmetric copulas were derived from them. Then, simulation data were obtained for these parameter values to determine the effect of asymmetry on data modeling, and directional dependency measures were found. In addition, the study methodology was applied to automobile bodily injury claims data, which is a real dataset with an asymmetric structure. Here, we used two different asymmetric models: the Khoudraji copula KC models, which are created by multiplying independent and Archimedean copulas, and the LCC models, which are linear-convex combinations of Archimedean copulas. Finally, the appropriate model was selected according to the directional dependency coefficients, and the results were interpreted. Copyright 2021, Yıldız Technical University.
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    The Statistical Analysis of the Earthquake Hazard for Turkey by Generalized Linear Models
    (Gazi Univ, 2017) Kizilok Kara, Emel; Durukan, Kubra
    In this paper, 4863 earthquake data of magnitude 4.0 and greater from 1900 to 2014 are statistically analyzed for the earthquake hazard in Turkey. The magnitude-frequency relationship in earthquake risk analysis is often performed by Gutenberg-Richter model. With the use of this model, information about earthquake potential of any region can be obtained by previous data and by estimating parameters such as return periods and possibilities of their occurrence. In this study, the relationship between earthquake numbers and magnitudes is modelled with the Generalized Linear Models as an alternative to Gutenberg-Richter model. Generalized Poisson Regression model and Generalized Negative Binomial Regression models as Generalized Linear Models are utilized in the study. Generalized Poisson Regression model is found as the best model when considering the dispersion parameters and model selection criteria. Exceeding probabilities and return periods are calculated for the selected years depending on yearly average occurrence number of earthquakes estimated with the Gutenberg-Richter and Generalized Poisson Regression models. According to the results, Generalized Poisson Regression model can be employed for seismic risk modelling in Turkey.