In this paper, we introduce a new smooth estimator for continuous distribution functions on the positive real half-line using Szasz-Mirakyan Operators. The approach is similar to the idea of the Bernstein estimator. 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 and in a simulation study.

翻译：在本文中,我们用Szasz-Mirakyan运算符为正半线连续分配功能引入一个新的平稳估算符。这个方法与伯恩斯坦测算仪的想法相似。我们显示,拟议的测算符在无症状(集成)平均差错方面优于经验分配功能,在理论比较和模拟研究方面与其他竞争者相比,通常优于其他竞争者。