Çift Sıralı Küme Örnekleme Tasarımı Altında Power Rayleigh Dağılımı Parametrelerinin Farklı Yöntemler ile Tahmini

Öz

Bu çalışmada, Basit Tesadüfi Örnekleme, Sıralı Küme Örneklemesi ve Çift Sıralı Küme Örneklemesi tasarımları altında parametre tahmini için Power Rayleigh dağılımının kullanımı incelenmiştir. Power Rayleigh dağılımına ilişkin parametrelerin tahmini için maksimum olabilirlik ve moment yöntemine dayalı tahmin edicileri tartışılmış ve bunların özellikleri basit rastgele örnekleme, sıralı küme örneklemesi ve çift sıralı küme örneklemesi tasarımları için analiz edilmiştir. Maksimum olabilirlik ve moment tahmin edicilerinin performanslarını yanlılıklar ve hata kare ortalamaları açısından değerlendirmek için kapsamlı bir Monte Carlo simülasyon çalışması yapılmıştır. Sonuçlar, çift sıralı küme örneklemesi altındaki moment tahmin edicisinin basit tesadüfi örnekleme ve sıralı küme örneklemesi tasarımlarından önemli ölçüde daha verimli olduğunu göstermektedir.

Anahtar Kelimeler

• Çift sıralı küme örneklemesi
• sıralı küme örneklemesi
• parametre tahmini
• Power Rayleigh dağılımı

Estimation of the Parameters of the Power Rayleigh Distribution Using Different Methods Under a Double Ranked Set Sampling Design

Öz

In this study, the use of the Power Rayleigh distribution for parameter estimation under simple random sampling, ranked set sampling and double ranked set sampling designs is investigated. Maximum likelihood and method of moment estimators for parameter estimation of the power Rayleigh distribution are discussed and their properties are analysed for the simple random sampling, ranked set sampling and double ranked set sampling designs. A comprehensive Monte Carlo simulation study was carried out to evaluate the performance of the maximum likelihood and moment estimators in terms of biases and mean square errors. The results show that the moment estimator under the double ranked set sampling desing is significantly more efficient than the simple random sampling and ranked set sampling designs.

Anahtar Kelimeler

• Double ranked set sampling
• ranked set sampling
• parameter estimation
• Power Rayleigh distribution

Kaynakça

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