Spatial clustering of extreme annual precipitation in Uruguay

The main objective of this work is to study the existence of spatial patterns maximum annual rainfall (through daily observations) within the territory of Uruguay and to show the application of two new statistical tools recently proposed. In the first stage, the distributions of maximum annual precipitation at each meteorological station will be studied. In the second stage, spatial clustering methods will be applied. To get the distribution of the maximum of each station, we have used a truncated Cram\'er-von Mises hypothesis test (the first statistical tool) and showed that it improves on the performance of the classic likelihood ratio test. It was found that in 18 study locations the distribution that best fits the data is of the Gumbel type, and for the other two, it is of the Fr\'echet type. Regarding the clustering methods, two methodologies were used, one of them was to perform clustering with the estimated parameters and the other was the PAM methodology using the F-madogram as distance, highlighting the homogeneity throughout the Uruguayan territory. Another novelty of this work (the second statistical tool) consists in including, as a complement to the clustering, the recently proposed independence test based on recurrence rates.