Parçacık Sürü Optimizasyon Algoritması Kullanılarak Nakagami Dağılımı için En Çok Olabilirlik Tahmini ve Uygulamaları

Yıl 2023, Cilt: 5 Sayı: 2, 209 - 218, 31.12.2023

Adi Omaia Faouri , Pelin Kasap

https://doi.org/10.47112/neufmbd.2023.19

Öz

Nakagami dağılımı, radyo sinyallerinin sönümlenmesini modellemek için ortaya çıkmıştır ve çeşitli disiplinlerde yaygın olarak kullanılmaktadır. Bu çalışmada, dağılımın şekil ve ölçek parametrelerini tahmin etmek için en çok olabilirlik (ML) tahmin yöntemi kullanılmıştır. Ancak, bu dağılım için olabilirlik denklemlerinin açık çözümleri bulunmamaktadır. Bu nedenle, bu denklemlerin çözümü için, parçacık sürüsü optimizasyon (PSO), genetik algoritma (GA) ve quasi-newton (QN) algoritmaları olmak üzere üç temel algoritma kullanılmıştır. Bu algoritmaların performanslarının karşılaştırmaları, yan, hata kareler ortalaması (MSE) ve eksiklik (DEF) kriterleri dikkate alınarak, kapsamlı bir Monte-Carlo simülasyon çalışması ile yapılmıştır. Model, kullanışlılığını göstermek amacıyla dört gerçek veri setine uygulanmıştır.

Anahtar Kelimeler

En çok olabilirlik, Nakagami dağılımı, Parçacık sürü optimizasyon

Maximum Likelihood Estimation for the Nakagami Distribution Using Particle Swarm Optimization Algorithm with Applications

Öz

The Nakagami distribution originated to model the fading of radio signals and is widely used in various disciplines. In this study, the maximum likelihood (ML) estimation method is used to estimate the shape and scale parameters of the distribution. However, there are no explicit solutions to the likelihood equations for this distribution. Therefore, three main algorithms, the particle swarm optimization algorithm (PSO), the genetic algorithm (GA), and the quasi-newton (QN) algorithm, have been used to solve these equations. Comparisons of the performances of these algorithms have been made with a comprehensive Monte-Carlo simulation study, taking into account the bias, mean squared error (MSE), and deficiency (DEF) criteria. The model has been applied to four real data sets in order to demonstrate its usefulness.

Anahtar Kelimeler

Maximum Likelihood, Nakagami Distribution, Particle swarm optimization, Monte-Carlo simulation

Kaynakça

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