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

Year 2025, Volume: 25 Issue: 6, 1316 - 1322

Mahmut Sami Erdoğan

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 polynomials , Rational Bernstein Polynomials , Parameter Estimation , Nonparametric Estimation , Mean Squared Error

Bernstein ve Rasyonel Bernstein Polinom Tabanlı Yaklaşımlar Kullanılarak Olasılık Dağılımlarının Parametre Tahmini

Abstract

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. Simülasyon sonuçları rasyonel Bernstein polinomlarının daha düşük ortalama karesel hata değerlerine ulaştığını ve bunun sonucunda artan esneklik yoluyla parametre kestirim doğruluğunu artırdığını göstermektedir.

Keywords

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

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