Asymmetric Kernels for Boundary Modification in Distribution Function Estimation

Abstract

Kernel-type estimators are popular in density and distribution function estimation. However, they suffer from boundary effects. In order to modify this drawback, this study has proposed two new kernel estimators for the cumulative distribution function based on two asymmetric kernels including the Birnbaum–Saunders kernel and the Weibull kernel. We show the asymptotic convergence of our proposed estimators in boundary as well as interior design points. We illustrate the performance of our proposed estimators using a numerical study and show that our proposed estimators outperform the other commonly used methods. The illustration of our proposed estimators to a real data set indicates that they provide better estimates than those of the formerly-known methodologies.