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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Volume 14, issue 11 | Copyright

Special issue: Advances in statistical hydrology

Hydrol. Earth Syst. Sci., 14, 2167-2175, 2010
https://doi.org/10.5194/hess-14-2167-2010
© Author(s) 2010. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 03 Nov 2010

Research article | 03 Nov 2010

On accuracy of upper quantiles estimation

I. Markiewicz, W. G. Strupczewski, and K. Kochanek I. Markiewicz et al.
  • Institute of Geophysics Polish Academy of Sciences, Warszawa, Poland

Abstract. Flood frequency analysis (FFA) entails the estimation of the upper tail of a probability density function (PDF) of annual peak flows obtained from either the annual maximum series or partial duration series. In hydrological practice, the properties of various methods of upper quantiles estimation are identified with the case of known population distribution function. In reality, the assumed hypothetical model differs from the true one and one cannot assess the magnitude of error caused by model misspecification in respect to any estimated statistics. The opinion about the accuracy of the methods of upper quantiles estimation formed from the case of known population distribution function is upheld. The above-mentioned issue is the subject of the paper. The accuracy of large quantile assessments obtained from the four estimation methods is compared to two-parameter log-normal and log-Gumbel distributions and their three-parameter counterparts, i.e., three-parameter log-normal and GEV distributions. The cases of true and false hypothetical models are considered. The accuracy of flood quantile estimates depends on the sample size, the distribution type (both true and hypothetical), and strongly depends on the estimation method. In particular, the maximum likelihood method loses its advantageous properties in case of model misspecification.

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