Commonly used statistical procedure to describe the observed statistical sets is to use their conventional moments or cumulants. When choosing an appropriate parametric distribution for the data set is typically that ...Commonly used statistical procedure to describe the observed statistical sets is to use their conventional moments or cumulants. When choosing an appropriate parametric distribution for the data set is typically that parameters of a parametric distribution are estimated using the moment method of creating a system of equations in which the sample conventional moments lay in the equality of the corresponding moments of the theoretical distribution. However, the moment method of parameter estimation is not always convenient, especially for small samples. An alternative approach is based on the use of other characteristics, which the author calls L-moments. L-moments are analogous to conventional moments, but they are based on linear combinations of order statistics, i.e., L-statistics. Using L-moments is theoretically preferable to the conventional moments and consists in the fact that L-moments characterize a wider range of distribution. When estimating from sample L-moments, L-moments are more robust to the presence of outliers in the data. Experience also shows that, compared to conventional moments, L-moments are less prone to bias of estimation. Parameter estimates obtained using L-moments are mainly in the case of small samples often even more accurate than estimates of parameters made by maximum likelihood method. Using the method of L-moments in the case of small data sets from the meteorology is primarily known in statistical literature. This paper deals with the use of L-moments in the case for large data sets of income distribution （individual data） and wage distribution （data are ordered to form of interval frequency distribution of extreme open intervals）. This paper also presents a comparison of the accuracy of the method of L-moments with an accuracy of other methods of point estimation of parameters of parametric probability distribution in the case of large data sets of individual data and data ordered to form of interval frequency distribution.展开更多
This paper focuses on the distributed parameter modeling of the zinc electrowinning process(ZEWP)to reveal the spatiotemporal distribution of concentration of zinc ions(CZI)and sulfuric acid(CSA)in the electrolyte.Con...This paper focuses on the distributed parameter modeling of the zinc electrowinning process(ZEWP)to reveal the spatiotemporal distribution of concentration of zinc ions(CZI)and sulfuric acid(CSA)in the electrolyte.Considering the inverse diffusion of such ions in the electrolyte,the dynamic distribution of ions is described by the axial dispersion model.A parameter estimation strategy based on orthogonal approximation has been proposed to estimate the unknown parameters in the process model.Different industrial data sets are used to test the effectiveness of the spatiotemporal distribution model and the proposed parameter estimation approach.The results demonstrate that the analytical model can effectively capture the trends of the electrolysis reaction in time and thus has the potential to implement further optimization and control in the ZEWP.展开更多
文摘Commonly used statistical procedure to describe the observed statistical sets is to use their conventional moments or cumulants. When choosing an appropriate parametric distribution for the data set is typically that parameters of a parametric distribution are estimated using the moment method of creating a system of equations in which the sample conventional moments lay in the equality of the corresponding moments of the theoretical distribution. However, the moment method of parameter estimation is not always convenient, especially for small samples. An alternative approach is based on the use of other characteristics, which the author calls L-moments. L-moments are analogous to conventional moments, but they are based on linear combinations of order statistics, i.e., L-statistics. Using L-moments is theoretically preferable to the conventional moments and consists in the fact that L-moments characterize a wider range of distribution. When estimating from sample L-moments, L-moments are more robust to the presence of outliers in the data. Experience also shows that, compared to conventional moments, L-moments are less prone to bias of estimation. Parameter estimates obtained using L-moments are mainly in the case of small samples often even more accurate than estimates of parameters made by maximum likelihood method. Using the method of L-moments in the case of small data sets from the meteorology is primarily known in statistical literature. This paper deals with the use of L-moments in the case for large data sets of income distribution （individual data） and wage distribution （data are ordered to form of interval frequency distribution of extreme open intervals）. This paper also presents a comparison of the accuracy of the method of L-moments with an accuracy of other methods of point estimation of parameters of parametric probability distribution in the case of large data sets of individual data and data ordered to form of interval frequency distribution.
基金Project(61673400)supported by the National Natural Science Foundation of ChinaProject(2015cx007)supported by the Innovation-driven Plan in Central South University,China+1 种基金Project(61321003)supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of ChinaProjects(61590921,61590923)supported by the Major Program of the National Natural Science Foundation of China
文摘This paper focuses on the distributed parameter modeling of the zinc electrowinning process(ZEWP)to reveal the spatiotemporal distribution of concentration of zinc ions(CZI)and sulfuric acid(CSA)in the electrolyte.Considering the inverse diffusion of such ions in the electrolyte,the dynamic distribution of ions is described by the axial dispersion model.A parameter estimation strategy based on orthogonal approximation has been proposed to estimate the unknown parameters in the process model.Different industrial data sets are used to test the effectiveness of the spatiotemporal distribution model and the proposed parameter estimation approach.The results demonstrate that the analytical model can effectively capture the trends of the electrolysis reaction in time and thus has the potential to implement further optimization and control in the ZEWP.
