On Estimating Parameters of the Kumaraswamy Distribution with Ranked Set Sampling Using Genetic Algorithms

Abstract

In this paper, genetic algorithm approach is used to estimate parameters of the Kumaraswamy distribution with maximum likelihood method. In addition ranked set sampling is used since it is expected to give better results in comparison to simple random sampling. Genetic algorithm approach is chosen because it is relatively more convenient in terms of satisfying positivity constraints for the parameters of the Kumaraswamy distribution. Also there is no need to use derivatives in the genetic algorithm approach. Bias, MSE and efficiency is calculated to compare performaces of maximum likelihood estimators for ranked set sampling and simple random sampling obtained by using genetic algorithms. The R software and related packages are preferred for calculations in the simulation study.

Keywords

• Kumaraswamy distribution,Ranked set sampling,Maximum likelihood estimation,Genetic algorithm,R software

Sıralı Küme Örneklemesi ile Kumaraswamy Dağılımı Parametrelerinin Tahmin Edilmesinde Genetik Algoritma Kullanılması

Abstract

Bu çalışmada, Kumaraswamy dağılımının parametrelerinin en çok olabilirlik yöntemi ile tahmin edilmesi genetik algoritma yaklaşımı kullanılarak araştırılmıştır. Ayrıca basit rasgele örneklemeye göre daha iyi sonuç verebileceği düşünülerek parametrelerin tahmin edilmesinde sıralı küme örneklemesi de incelenmiştir. Genetik algoritma yaklaşımı, Kumaraswamy dağılımı parametrelerinin pozitif olma koşulunun hesaba katılması nedeniyle tercih edilmiştir. Ek olarak genetik algoritma yaklaşımında en çok olabilirlik fonksiyonunun türev bilgisine ihtiyaç duyulmaması da hesaplamalarda kolaylık sağlamaktadır. Genetik algoritma kullanılarak elde edilen her iki örnekleme yöntemine ait olabilirlik tahmin edicilerinin performanslarının karşılaştırılması için yan, hata kareler ortalaması ve etkinlikleri hesaplanmıştır. Simülasyon çalışmasındaki hesaplamalar için R yazılımı ve ilgili paketler kullanılmıştır.

Keywords

• Kumaraswamy dağılımı,Sıralı küme örneklemesi,En çok olabilirlik tahmini,Genetik algoritma

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