Archimedean kopula modelleri için yeni bir uyum iyiliği yaklaşımı ve güç analizi

In this thesis, a new class of bivariate multi-parameter Archimedean copula based on Kendall distribution using Bernstein-Bezier polynomials is introduced. This new class copula has flexible dependence properties depending on the polynomial degree and the control points. Some dependence characteristics such as Kendall's tau, upper tail and lower tail dependence of the this new Archimedean copula class are derived. The simulation procedure based on these desired dependence characteristics is presented. Also, we propose an estimation method for the Archimedean family of copula in a nonparametric setting. Bernstein polynomials and Bezier curve approaches are used to estimate the Kendall distribution function of the Archimedean copula. Also, a new goodness-of-fit test based on Cramer-Von Mises type statistic is constructed using new estimation methods of Kendall distribution function. A Monte Carlo study is performed to measure the performance of the proposed tests. The simulation results show that both the Bernstein polynomial and the B\'ezier curve based tests have better performances than the classical one since they have flexible form according to its order m.