On the estimate and scaling of GP and GEV parameters and laws

In this work we outline robust techniques, based on linear combinations of "selected" Order Statistics, to estimate both the position and the scale parameters of Generalized Pareto and Generalized Extreme Value distributions. Furthermore, we consider the theoretical relations linking the parameters of these two distributions, and temporal scaling properties are shown to hold for both laws when considering proper power-law forms for both the position and the scale parameters. Also shown is (i) the relation between the scaling exponents of the distributions of interest, (ii) how the scaling properties of one distribution yield those of the other, and (iii) how the scaling features may be used to estimate the parameters of the distributions at different temporal scales.