Generalized Exponential Distribution in Flood Frequency Analysis for Polish Rivers

PLoS One. 2015 Dec 10;10(12):e0143965. doi: 10.1371/journal.pone.0143965. eCollection 2015.


Many distributions have been used in flood frequency analysis (FFA) for fitting the flood extremes data. However, as shown in the paper, the scatter of Polish data plotted on the moment ratio diagram shows that there is still room for a new model. In the paper, we study the usefulness of the generalized exponential (GE) distribution in flood frequency analysis for Polish Rivers. We investigate the fit of GE distribution to the Polish data of the maximum flows in comparison with the inverse Gaussian (IG) distribution, which in our previous studies showed the best fitting among several models commonly used in FFA. Since the use of a discrimination procedure without the knowledge of its performance for the considered probability density functions may lead to erroneous conclusions, we compare the probability of correct selection for the GE and IG distributions along with the analysis of the asymptotic model error in respect to the upper quantile values. As an application, both GE and IG distributions are alternatively assumed for describing the annual peak flows for several gauging stations of Polish Rivers. To find the best fitting model, four discrimination procedures are used. In turn, they are based on the maximized logarithm of the likelihood function (K procedure), on the density function of the scale transformation maximal invariant (QK procedure), on the Kolmogorov-Smirnov statistics (KS procedure) and the fourth procedure based on the differences between the ML estimate of 1% quantile and its value assessed by the method of moments and linear moments, in sequence (R procedure). Due to the uncertainty of choosing the best model, the method of aggregation is applied to estimate of the maximum flow quantiles.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Floods*
  • Likelihood Functions
  • Models, Theoretical*
  • Normal Distribution
  • Poland
  • Rivers

Grant support

This work was partly financed by the grant of the Polish National Science Centre titled “Modern statistical models for analysis of flood frequency and features of flood waves“, decision nr DEC-2012/05/B/ST10/00482 and by the Polish Ministry of Science and Higher Education under the Grant Iuventus Plus IP 2010 024570 titled “Analysis of the efficiency of estimation methods in flood frequency modelling”. This work was partially supported within statutory activities No 3841/E-41/S/2015 of the Ministry of Science and Higher Education of Poland.