Smooth Distribution Function Estimation for Lifetime Distributions using Szasz-Mirakyan Operators

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.Comment: Small typo in Theorem 10: Now -1/12 instead of +1/12 in the term of order $m^{-1}