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

Year 2019, Volume: 23 Issue: 2, 367 - 373, 25.08.2019

Adil Kılıç , Güvenç Arslan

https://doi.org/10.19113/sdufenbed.471565

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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