Parameter Estimation of Probability Distributions Using Bernstein and Rational Bernstein Polynomial-Based Approaches

Authors : Mahmut Sami Erdoğan

Pages : 1316-1322

Doi:10.35414/akufemubid.1644551

View : 71 | Download : 217

Publication Date : 2025-12-03

Article Type : Research Paper

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.
Keywords : Bernstein polinomları, Rasyonel Bernstein polinomları, Parametre kestirimi, Parametrik olmayan kestirim, Ortalama karesel hata

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