copula function

In this article a spatial model is presented for extreme values with marginal generalized extreme value (GEV) distribution. The spatial model would be able to capture the multi-scale spatial dependencies. The small scale dependencies in this model is modeled by means of copula function and then in a hierarchical manner a random field is related to location parameters of marginal GEV distributions in order to account for large scale dependencies. Bayesian inference of presented model is accomplished by offered Markov chain Monte Carlo (MCMC) design، which consisted of Gibbs sampler، random walk Metropolis-Hastings and adaptive independence sampler algorithms. In proposed MCMC design the vector of location parameters is updated simultaneously based on devised multivariate proposal distribution. Also، we attain Bayesian spatial prediction by approximation of the predictive distribution. Finally، the estimation of model parameters and possibilities for capturing and separation of multi-scale spatial dependencies are investigated in a simulation example and analysis of wind speed extremes.

One of the fundamental steps in management of drought involves identification and frequency analysis of its properties, e.g. duration and severity of drought. Regarding the high correlation among these factors, one must use a method that shows the relation and effects of these factors on drought analysis. Copula functions can be used to represent the dependency structure of several variables through a model. In this paper, we introduce the appropriate copula families for modeling drought phenomenon modeling. Then, their parameters would be estimated by maximum likelihood and Empirical Bayes methods and the most appropriate copula function for determining bivariate distribution of duration and severity of drought in Tehran stations is determined. Next, this copula function is used to model the drought phenomenon of Tehran for the period of 37 years from 1348 until 1384, Finaly the application of this model is represented in water supply management.