A simple approximation to multifractal rainfall maxima using a generalized extreme value distribution model

Among different approaches that have been proposed to explain the scaling structure of temporal rainfall, a significant body belongs to models based on sequences of independent pulses with internal multifractal structure. Based on a standard asymptotic result from extreme value theory, annual rainfall maxima are typically modelled using a generalized extreme value (GEV) distribution. However, multifractal rainfall maxima converge slowly to a GEV shape, with important shape-parameter estimation issues, especially from short samples. The present work uses results from multifractal theory to propose a solution to the GEV shape-parameter estimation problem, based on an iterative numerical procedure.