Statistical modelling of annual maximum flows in Turkish rivers

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Abstract
The lognormal, Gumbel, smemax, log-Boughton, log-logistic, Pearson-3 and log-Pearson-3 distributions are applied to the annual flood peaks series longer than 21 observations of 112 unregulated natural streams in 23 major basins in Turkey. The parameters of most of those distributions are estimated by the methods of: (a) moments; (b) maximum likelihood; and (c) probability weighted moments. A detailed chi-squared goodness-of-fit test is performed both with equal-length sliced histograms and with equal-probability-area sliced histograms, each one being repeated three times for three different but consecutively increasing slice numbers, such as 5, 6, 7 or 6, 7, 8 etc. A Kolmogorov-Smirnov goodness-of-fit test is also included. According to the evaluations of those three tests, a single definite distribution did not appear to be the best consistently for all the sample series taken, but the log-logistic and log-Pearson-3 models scored a larger number of better fits.