In this paper, a new estimator of the shape parameter in the family of Gamma distribution is constructed by using the moment idea, and it is proved that this estimator is strongly consistent and asymptotically normal.
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 deals with the development of sample characteristics of wage distribution in recent years in the Czech Republic by the highest educational attainment. Gross monthly wage is the variable investigated. We dis...This paper deals with the development of sample characteristics of wage distribution in recent years in the Czech Republic by the highest educational attainment. Gross monthly wage is the variable investigated. We distinguish the following scale of the highest educational attainment： primary and incomplete education, secondary education without GCSE, secondary education with GCSE, higher vocational and bachelor education and tertiary education. Forecasts of wage distribution have been developed for the next two years for all of these categories. Three-parametric lognormal curve formed the basis of the theoretical probability distribution. Parameter values of relevant three-parametric lognormal curves were then estimated using the method of L-moments of parameter estimation. Forecasts of sample values of L-moments were calculated using trend analysis of their past development and the parameters of three-parametric Iognormal curves for forecasts of wage distribution were calculated using the predicted values of the first three sample L-moments. We have obtained the forecasts of wage distribution by the highest educational attainment on the basis of these probability density functions.展开更多
文摘In this paper, a new estimator of the shape parameter in the family of Gamma distribution is constructed by using the moment idea, and it is proved that this estimator is strongly consistent and asymptotically normal.
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.
文摘This paper deals with the development of sample characteristics of wage distribution in recent years in the Czech Republic by the highest educational attainment. Gross monthly wage is the variable investigated. We distinguish the following scale of the highest educational attainment： primary and incomplete education, secondary education without GCSE, secondary education with GCSE, higher vocational and bachelor education and tertiary education. Forecasts of wage distribution have been developed for the next two years for all of these categories. Three-parametric lognormal curve formed the basis of the theoretical probability distribution. Parameter values of relevant three-parametric lognormal curves were then estimated using the method of L-moments of parameter estimation. Forecasts of sample values of L-moments were calculated using trend analysis of their past development and the parameters of three-parametric Iognormal curves for forecasts of wage distribution were calculated using the predicted values of the first three sample L-moments. We have obtained the forecasts of wage distribution by the highest educational attainment on the basis of these probability density functions.
