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EN
Vessel passage speed is one of the parameters describing the vessel traffic stream on a selected waterway. Knowing the probability distribution of vessel passage speeds is essential for modeling vessel traffic streams on a waterway. This article undertakes probabilistic modeling for vessel speeds in restricted areas, where the distribution of the vessel passage time of the waterway section is known. The probabilistic procedure of the inverse random variable is used. Four different cases are considered. First, the probabilistic distribution of the vessel passage speed is given, where the vessel passage time is described by the normal distribution in certain restricted areas. The next three cases present the probabilistic distribution of vessel passage speeds on the Szczecin–Świnoujście fairway, where the vessel passage time is described by the extreme value distribution, the Frèchet distribution and the Weibull distribution.
EN
The scope of this study was to assess the usefulness of top probability distributions to describe maximum rainfall data in the Lusatian Neisse River basin, based on eight IMWM-NRI meteorological stations. The research material was composed of 50-year precipitation series of daily totals from 1961 to 2010. Misssing measurement data were estimated using a weighted average method. Homogeneity for refilled data were investigated by precipitation double aggregation curve. Correlation between the measurement data varied from 96 to 99% and did not indicate a violation of the homogeneity of rainfall data series. Variability of recorded daily precipitation maxima were studied by linear regression and non-parametric Mann-Kendall tests. Long-term period changes at maximum rainfalls for four stations remained statistically insignificant, and for the other four were significant, although the structure of maximums was relatively similar. To describe the measured data, there were used the Fréchet, Gamma, Generalized Exponential Distribution (GED), Gumbel, Log-normal and Weibull distributions. Particular distribution parameters were estimated using the maximum likelihood method. The conformity of the analyzed theoretical distributions with measured data was inspected using the Schwarz Bayesian information criterion (BIC) and also by the relative residual mean square error (RRMSE). Among others, the Gamma, GED, and Weibull distributions fulfilled the compliance criterion for each meteorological station respectively. The BIC criterion indicated GED as the best; however differences were minor between GED on the one hand and the Gamma and Weibull distributions on the other. After conducting the RRMSE analysis it was found that, in comparison to the other distributions, GED best describes the measured maximum rainfall data.
EN
In this paper, the results of a study of key sectors of Polish economy based on maximum entropy principle and concept of inverse important coefficients are presented. These methods were applied to Polish input-output tables in aggregations 15*15 and 31*31. For these aggregations a taxonomy of industries of Polish economy at different time points was established.
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