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Max-stable processes play a fundamental role in modeling the spatial dependence of extremes because they appear as a natural extension of multivariate extreme value distributions. In practice, a well-known restrictive assumption when using max-stable processes comes from the fact that the observed extremal dependence is assumed to be related to a particular max-stable dependence structure. As a consequence, the latter is imposed to all events which are more extreme than those that have been observed. Such an assumption is inappropriate in the case of asymptotic independence. Following recent advances in the literature, we exploit a max-mixture model to suggest a general spatial model which ensures extremal dependence at small distances, possible independence at large distances and asymptotic independence at intermediate distances. Parametric inference is carried out using a pairwise composite likelihood approach. Finally we apply our modeling framework to analyze daily precipitations over the East of Australia, using block maxima over the observation period and exceedances over a large threshold. [ABSTRACT FROM AUTHOR]

Abstract: The Pareto distribution is found in a large number of real world situations and is also a well-known model for extreme events. In the spirit of Neyman [1937. Smooth tests for goodness of fit. Skand. Aktuarietidskr. 20, 149–199] and Thomas and Pierce [1979. Neyman''s smooth goodness-of-fit test when the hypothesis is composite. J. Amer. Statist. Assoc. 74, 441–445], we propose a smooth goodness of fit test for the Pareto distribution family which is motivated by LeCam''s theory of local asymptotic normality (LAN). We establish the behavior of the associated test statistic firstly under the null hypothesis that the sample follows a Pareto distribution and secondly under local alternatives using the LAN framework. Finally, simulations are provided in order to study the finite sample behavior of the test statistic. [Copyright &y& Elsevier]