UM and extremes
The UM model can be used to estimate the critical moment and introduced previously. The estimation is performed from the sampling space , the dimension quantify the extension of the probability space. Lets the realization or the available sampling. We observe observation with :
The co-dimension of the maximum singularity is given by :
The singularities characterized by a co-dimension larger then can not be observed. The statistical moment can be deduced from the following equation:
In the multifractal framework we obtain :
When the upper limit of the UM model is the divergence of the statistical moment, the divergence order is the solution of :