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.