University of Tehran Journal of Sciences, Islamic Republic of Iran 1016-1104 34 4 2023 12 01 Beta Kernel Estimator for a Cumulative Distribution Function with Bounded Support 349 361 96219 10.22059/jsciences.2024.367933.1007836 EN Behzad Mansouri Department of Statistics, Shahid Chamran University of Ahvaz, Ahvaz,Islamic Republic of Iran Azam Rastin Department of Statistics, Shahid Chamran University of Ahvaz, Ahvaz,Islamic Republic of Iran Habib Allah Mombeni Department of Statistics, Shahid Chamran University of Ahvaz, Ahvaz,Islamic Republic of Iran Journal Article 2023 11 20 Kernel estimation of the cumulative distribution function (CDF), when the support of the data is bounded, suffers from bias at the boundaries. To solve this problem, we introduce a new estimator for the CDF with support (0,1) based on the beta kernel function. By studying the asymptotic properties of the proposed estimator, we show that it is consistent and free from boundary bias. We conducted an extensive simulation to illustrate the performance of the proposed estimator. The results demonstrate the superiority of the proposed estimator over other commonly used estimators. As an application, we use the estimated CDF for nonparametric simulation. Using a numerical study, we show that the performance of the kernel probability density function (PDF) estimation in which a large sample simulated from the estimated CDF is employed can be noticeably improved. We also use the proposed estimator to estimate the CDF of the household health cost in Iran in 2019. https://jsciences.ut.ac.ir/article_96219_3b53bf4d214c48a830522a813de61c0c.pdf