Chapter
Apr 26, 2012
Some Parameter Estimators in the Generalized Pareto Model and Their Inconsistency with Observed Data
Publication: World Environmental and Water Resources Congress 2007: Restoring Our Natural Habitat
Abstract
The generalized Pareto distribution (GPD) is widely used in the frequency modeling of hydrological extremes. Statistical methods used to fit this model to data include the methods of maximum likelihood (ML), of moments (MM), of probability weighted moments (PWM), and of generalized probability weighted moments (GPWM). When the shape parameter of the GPD is positive, the sample space is a finite interval whose upper bound depends on the distribution parameters. The MM, PWM and GPWM methods may produce estimates of this upper bound that are inconsistent with the observed data. This inconsistency occurs when one or more sample observations exceed the estimated upper bound, thus making this estimated upper bound physically unjustifiable. In this paper we shed more light on this problem of inconsistency with the data and examine its consequences by using Monte Carlo simulation. We provide new guidelines for choosing between the ML, MM, PWM and GPWM methods for estimating GPD quantiles.
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© 2007 American Society of Civil Engineers.
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Published online: Apr 26, 2012
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Department of Mathematics and Statistics, Université de Moncton, Moncton, N.B., Canada, E1A 3E9. E-mail: [email protected]
Department of Mathematics and Statistics, Université de Moncton, Moncton, N.B., Canada, E1A 3E9. E-mail: [email protected]
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