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Generalized probability weighted moments: Application to the generalized Pareto Distribution
Author(s) -
Rasmussen Peter F.
Publication year - 2001
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2001wr900014
Subject(s) - mathematics , quantile , generalized pareto distribution , distribution (mathematics) , class (philosophy) , pareto principle , generalized method of moments , pareto distribution , type (biology) , method of moments (probability theory) , probability distribution , statistics , mathematical optimization , estimator , mathematical analysis , extreme value theory , computer science , ecology , artificial intelligence , biology
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[XF j ] (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.