Simulated Analysis Of Bivariate Extreme Mixed Model

In recent years, extreme value theory has developed rapidly , and is becoming widely used in many other disciplines. It is important in practice. In this paper, we firstly introduce some basic concepts of extreme value theory, which includes the development and application of extreme value theory, the concept, threshold choice, maximum likelihood estimation of univariate extreme value theory and several bivariate extreme value models and behavior. Secondly, we emphasize on analysis of bivariate extreme mixed model. Bivariate extreme mixed model can not reach the complete dependence of extreme variables, so it has a restriction in application. However,in some range of dependence bivariate extreme mixed model is still a good model. Specifically, we give some basic knowledge about bivariate extreme mixed model and the method of generating stochastic data. We aim to assess the effects of dependence parameter and marginal parameters through a simulation study when a BEV distribution with mixed model dependence is fitted to data from other bivariate extreme value copula. As a result, if we measure dependence by Kendall's r, we find that to some extent mixed model can capture the dependence of other models, and for asymptotically independent model, the bias in the marginal parameters is not severe. Finally, we use mixed conditional model and GEV conditional model to analyze the dependence on risk of the data about the day log-daily returns of two exchange rates: UK sterling against both the US dollar and the Canadian dollar. It is important to avoid risk for foreign exchange market .