Optimisation of average rainfall estimation using copulas

Average rainfall estimation over a watershed can be viewed as a multivariate problem. Multivariate distributions are difficult to work with for estimation and decision making especially when the individual variables do not have Gaussian distributions. The complexity of the problem can be considerably reduced by using the technique of copulas, whereby working with marginal distributions computations are simplified to the level of univariate case. In this paper the copula functions are explored and illustrated with a specific application to rainfall estimation of a small catchment in Western Australia.