Mathematical Measure Of Middle-income Range

In this article, combined with the current Chinese situation, the method to define the concept of medium income group is proposed. Meanwhile, Medium income group, which is different from the middle class, is defined by medium income groups. This is not only convenient, but also in line with the current mainstream ideology of the medium income group.Considered the curve of gamma distribution density function and the curve of the experience income distribution density function is much similar, the fitting on the gamma distribution model for the Lorenz curve is put forward. Moreover, the medium income groups could be calculated by using the relationship between the proportion of medium income groups and Gene coefficient.To make up for the shortcomings of income data sparse, the data was subjected to KS test by using statistical methods in classical stochastic simulation, and then the middle-income range is presented by improving the income space law with the proportion of middle income.The population space method is improved, as the mean value of 40% of the income proportion for the lower limit of middle-income interval, and the last 40% for the upper limit of the interval, which is in line with its dynamic nature, and is convenient for different regions and different years to compare.The subordinate of membership function of fuzzy mathematics is used to compare the medium income, which could establish the membership functions of medium income. Each membership function correspond to income is the degree of membership and the overall membership is defined as “Middle-income population index”. The higher index is, the more the relative amount of middle-income population is.Finally using the relationship between the Engel’s coefficient Y and the medium income interval, the income interval corresponding to the internationally used 30% ?Y ?40% is the medium income interval. Meanwhile, when in the process of back stepping medium income interval, China’s actual conditions must be clear and the real factors should be considered.