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Physics of flood frequency analysis. II. Convective diffusion model versus lognormal model

Strupczewski W., Singh V., Węglarczyk S., Mitosek H.

Acta Geophysica Polonica

2003

Vol. 51, nr 1

85-106

The similarity between the convective diffusion (CD) model and the lognormal (LN) distribution is shown by comparison of their moment estimates. Both models are tested using annual peak discharges observed at 39 gauging-sections of Polish rivers. The average value of the ration of the coefficient of skew ness to the coefficient of variation equals about 2.52, a value closer to the ration of the CD model than to the gamma or the lognormal model. The likelihood ratio indicates the preference of the CD over the LN model for 27 out of 39 cases. Applying the maximum likelihood (ML) method, one should take into account the consequence of the wrong distributional assumption on the estimate of moments. In the case of CD, the ML-estimate of the means is unbiased for any true distribution, which is not the case with the LN model, moreover the ML-estimate of the two fist moments of CD remains asymptotically unbiased if LN is true, while there is small bias in the opposite case. To check the objectivity of our inferences from empirical findings, a simulation experiment was carried out, which comprised generated CD- and LN- distributed samples and both the moment and likelihood criteria for the distribution choice. Its results clearly show that normal hydrological sample sizes are far too small for selecting the true distribution.

Metoda momentów ważonych prawdopodobieństwem i L-momentów

Mitosek H.

Przegląd Geofizyczny

1998

R.43, z.3-4

165-182

Probability weighted moments and L-moments are discussed as another way to summarize the statistical properties of hydrological data. The conventional moments, extensively used in hydrology, have been appeared to be highly biased characteristics since 1974. For that reason, the probability weighted moments and the L-moments have been proposed as simple and reasonable efficient estimators of distribution's parameters and quantiles.