Tunable Combined Polynomial Model and Optimal Approximation to Lorentz Curve
The Lorentz curve of income group data is fitted with finite n degree ordinary algebraic polynomial,which often faces two problems:The end value is not closed and the fitting accuracy is not high.The tunable combined polynomial(TCP)proposed in this paper provides a way to solve these two problems.TCP model has the characteristic of"one main and two auxiliary"combination structure.The principal structure is an exponential polynomial with an impermanent number and a variable p as a power base.The two auxiliary components are:Add a term"specific highest power"pN to the end of the polynomial with an equal exponential power;Multiply each power function by an E(p)exponential factor with a tunable parameter T;Finally,a polynomial with pnE(p)combined function as the regression variable is formed.TCP model fitting packet data adopts the"Zhuangzi segmentation method"search and approximation mechanism:In the process of multiple linear regression,the optimal tuning parameter T integer value is searched in the interval of[0,128]based on the principle of minimizing the mean square error,so that there is good harmony between the pnE(p)regressors of the TCP model and the given packet data,so as to achieve the best approximation to the Lorentz curve of the packet data.The comparison experiment shows that the TCP model fits the 2013 National Postgraduate Mathematical Contest in Modeling E question data and the CPS data of the United States(1977,1990),and the mean square error MSE reaches the level of 10-9.The mean square error MSE for fitting the grouped data of 19 countries is on the order of 10-7～10-9.The fitting accuracy,adaptability and robustness of TCP model to different packet data are superior to the comparison model.
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