Ağırlık fonksiyonlarının Birnbaum–Saunders parametrelerinin ağırlıklı en küçük kareler tahminine etkileri

Abstract

Bu çalışmada, Birnbaum–Saunders dağılımının şekil ve ölçek parametrelerinin tahmininde, beş farklı ağırlık fonksiyonu kullanılarak elde edilen ağırlıklı en küçük kareler tahmin edicilerinin performansları karşılaştırılmıştır. Farklı parametre değerleri ve örneklem büyüklükleri için yürütülen Monte Carlo simülasyon çalışmasında, tahmin ediciler mutlak yanlılık ve hata kareler ortalaması ölçütleri bakımından değerlendirilmiştir. Ayrıca gözlemlerin belirli oranlarda aykırı değerlerle değiştirilmesinin parametre tahminleri üzerindeki etkisi incelenmiştir. Yöntemlerin uygulanabilirliğini göstermek amacıyla alüminyum numunelerin yorulma ömürlerine ilişkin bir veri seti analiz edilmiştir. Simülasyon ve gerçek veri analizinden elde edilen bulgular, ağırlık fonksiyonu seçiminin tahmin performansını ve aykırı değerlere duyarlılığı etkilediğini göstermektedir.

Keywords

• Birnbaum–Saunders dağılımı
• Ağırlıklı en küçük kareler
• Parametre tahmini
• Ağırlık fonksiyonları
• Aykırı değerler
• Monte Carlo simülasyonu.

Effects of weight functions on weighted least squares estimation of Birnbaum–Saunders parameters

Abstract

This study compares the performance of weighted least squares estimators obtained using five different weight functions for estimating the shape and scale parameters of the Birnbaum–Saunders distribution. A Monte Carlo simulation study is conducted for different parameter values and sample sizes, and the estimators are evaluated using absolute bias and mean squared error. The effect of replacing specified proportions of observations with outliers on parameter estimation is also examined. To illustrate the applicability of the methods, a dataset on the fatigue life of aluminum specimens is analyzed. The simulation and real-data findings show that the choice of weight function affects estimation performance and sensitivity to outliers.

Keywords

• Birnbaum–Saunders distribution
• Weighted least squares
• Parameter estimation
• Weight functions
• Outliers
• Monte Carlo simulation

References

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