In this paper, we introduce a new smooth estimator for continuous distribution functions on the positive real half-line using Szasz-Mirakyan operators, similar to Bernstein's approximation theorem. We show that the proposed estimator outperforms the empirical distribution function in terms of asymptotic (integrated) mean-squared error, and generally compares favourably with other competitors in theoretical comparisons. Also, we conduct the simulations to demonstrate the finite sample performance of the proposed estimator.

翻译：在本文中,我们引入了一个新的光滑测算器,用于使用Szasz-Mirakyan操作员,类似于Bernstein的近似理论理论,在正线实际半线上连续分配功能。我们显示,拟议的测算仪在无药用(集成)平均错数方面优于经验分配功能,在理论比较方面一般优于其他竞争者。此外,我们还进行模拟,以展示拟议的测算仪的有限样本性能。