@article{article_1644551, title={Parameter Estimation of Probability Distributions Using Bernstein and Rational Bernstein Polynomial-Based Approaches}, journal={Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi}, volume={25}, pages={1316–1322}, year={2025}, author={Erdoğan, Mahmut Sami}, keywords={Bernstein polynomials, Rational Bernstein Polynomials, Parameter Estimation, Nonparametric Estimation, Mean Squared Error}, abstract={This study examines two different approaches based on Bernstein polynomials and rational Bernstein polynomials for parameter estimation of probability distributions. It is discussed how both methods can be used in the parameter estimation process, and it is aimed to determine the optimal parameters with the least squares method. Monte Carlo simulations are performed to evaluate the effectiveness of the methods, and their estimation performances are analyzed for various distributions. Simulation results demonstrate that rational Bernstein polynomials achieve lower mean squared error values, which consequently raise parameter estimation accuracy through enhanced flexibility.}, number={6}, publisher={Afyon Kocatepe University}