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 favorably with other competitors in theoretical comparisons. Also, we conduct the simulations to demonstrate the finite sample performance of the proposed estimator.

中文翻译：

---

使用Szasz–Mirakyan算子对寿命分布进行平滑分布函数估计

在本文中，我们使用Szasz-Mirakyan算子为正实半线上的连续分布函数引入了一种新的平滑估计器，类似于Bernstein逼近定理。我们表明，在渐近（积分）均方误差方面，拟议的估计量优于经验分布函数，并且在理论比较中通常可与其他竞争者相比。此外，我们进行仿真以证明拟议估计量的有限样本性能。