TY - JOUR T1 - Parameter Estimation of Probability Distributions Using Bernstein and Rational Bernstein Polynomial-Based Approaches TT - Bernstein ve Rasyonel Bernstein Polinom Tabanlı Yaklaşımlar Kullanılarak Olasılık Dağılımlarının Parametre Tahmini AU - Erdoğan, Mahmut Sami PY - 2025 DA - November Y2 - 2025 JF - Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi PB - Afyon Kocatepe University WT - DergiPark SN - 2149-3367 SP - 1316 EP - 1322 VL - 25 IS - 6 LA - en AB - 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. KW - Bernstein polynomials KW - Rational Bernstein Polynomials KW - Parameter Estimation KW - Nonparametric Estimation KW - Mean Squared Error N2 - Bu çalışmada olasılık dağılımlarının parametre kestirimi için Bernstein polinomları ve rasyonel Bernstein polinomlarına dayalı iki farklı yaklaşım incelenmektedir. Her iki yöntemin parametre kestirim sürecinde nasıl kullanılabileceği tartışılmakta ve en küçük kareler yöntemi ile optimum parametrelerin belirlenmesi amaçlanmaktadır. Yöntemlerin etkinliğini değerlendirmek için Monte Carlo simülasyonları gerçekleştirilmekte ve çeşitli dağılımlar için kestirim performansları analiz edilmektedir. 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