Prediction in Partial Duration Series With Generalized Pareto-Distributed Exceedances

Dan Rosbjerg, Henrik Madsen, Peter Funder Rasmussen

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    Abstract

    As a generalization of the common assumption of exponential distribution of the exceedances in Partial duration series the generalized Pareto distribution has been adopted. Estimators for the parameters are presented using estimation by both method of moments and probability-weighted moments. The corresponding estimators for the T-year event are given and approximate expressions for bias and variance of the estimators are derived in both cases. Using the mean square error of the T-year event estimator as a performance index it is shown that the method of moments is preferable to the probability-weighted moments. Maintaining the generalized Pareto distribution as the parent exceedance distribution the T-year event is estimated assuming the exceedances to be exponentially distributed. For moderately long-tailed exceedance distributions and small to moderate sample sizes it is found, by comparing mean square errors of the T-year event estimators, that the exponential distribution is preferable to the correct generalized Pareto distribution despite the introduced model error and despite a possible rejection of the exponential hypothesis by a test of significance. For moderately short-tailed exceedance distributions (with physically justified upper limit) the correct exceedance distribution should be applied despite a possible acceptance of the exponential assumption by a test of significance.
    Original languageEnglish
    JournalWater Resources Research
    Volume28
    Issue number11
    Pages (from-to)3001-3010
    ISSN0043-1397
    Publication statusPublished - 1992

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