The estimation of the distribution function of a real random variable is an intrinsic topic in non parametric estimation. To this end, a distribution estimator based on Lagrange polynomials and Tchebychev-Gauss points, is introduced. Some asymptotic properties of the proposed estimator are investigated, such as its asymptotic bias, variance, mean squared error and Chung-Smirnov propriety. The asymptotic normality and the uniform convergence of the estimator are also established. Lastly, the performance of the proposed estimator is explored through a certain simulation examples.

中文翻译：

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使用拉格朗日多项式和 Tchebychev-Gauss 点估计分布函数

真实随机变量分布函数的估计是非参数估计中的一个固有主题。为此，引入了基于拉格朗日多项式和 Tchebychev-Gauss 点的分布估计器。研究了所提出的估计器的一些渐近特性，例如它的渐近偏差、方差、均方误差和 Chung-Smirnov 特性。也建立了估计量的渐近正态性和一致收敛性。最后，通过特定的模拟示例探索了所提出的估计器的性能。