Generalized probability weighted moments: Application to the generalized Pareto distribution

Probability weighted moments (PWMs) are widely used in hydrology for estimating parameters of flood distributions. The classical PWM approach considers 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 estimated. The classical approach is here compared with an extended class of PWMs that does not restrict j or k to be small nonnegative integers. Estimation based on the extended class of PWMs is named the generalized method of PWMs to distinguish it from the classical procedure. To illustrate the method, we consider estimation of quantiles in the generalized Pareto distribution and demonstrate that substantial gain in estimation accuracy can be obtained by using generalized PWMs.