Generalized probability weighted moments: Application to the generalized Pareto distribution

Probability weighted moments (PWMs) are widely used in hydrology for estima ting parameters of flood distributions. The classical PWM approach consider s moments of the type E[XFj] (or, alternatively, E[X(1 - F)(k)]), where j ( or k) takes values 0, 1, or 2 depending on the number of parameters to be e stimated. The classical approach is here compared with an extended class of PWMs that does not restrict j or k to be small nonnegative integers. Estim ation based on the extended class of PWMs is named the generalized method o f PWMs to distinguish it from the classical procedure. To illustrate the me thod, we consider estimation of quantiles in the generalized Pareto distrib ution and demonstrate that substantial gain in estimation accuracy can be o btained by using generalized PWMs.