In this paper, we study the complete convergence and complete moment convergence for weighted sums of extended negatively dependent (END) random variables under sub-linear expectations space with the condition of , further , ( is a slow varying and monotone nondecreasing function). As an application, the Baum-Katz type result for weighted sums of extended negatively dependent random variables is established under sub-linear expectations space. The results obtained in the article are the extensions of the complete convergence and complete moment convergence under classical linear expectation space.

In this paper, using the 2011 national economic accounting data of the provinces, we evaluated the government department performance by factor analysis. And then calculated the local government department's total output taking advantage of the labor production efficiency. And the labor production efficiency of government department concludes the performance information. Which will improved the method of accounting government department's output by cost.