  We proposed a semi-parametric estimation procedure in order to estimate the
parameters of a max-mixture model and also of a max-stable model (inverse
max-stable model) as an alternative to composite likelihood. A good estimation
by the proposed estimator required the dependence measure to detect all
dependence structures in the model, especially when dealing with the
max-mixture model. We overcame this challenge by using the F-madogram. The
semi-parametric estimation was then based on a quasi least square method, by
minimizing the square difference between the theoretical F-madogram and an
empirical one. We evaluated the performance of this estimator through a
simulation study. It was shown that on an average, the estimation is performed
well, although in some cases, it encountered some difficulties. We apply our
estimation procedure to model the daily rainfalls over the East Australia.
