Robust Estimators of the Shape Parameter of Weibull Distribution Based on Progressively Censored Sample

Abstract

Parameter estimation is a very important issue in lifetime models. The data type encountered in practice is usually in the form of progressive censored data. Parameter estimation based on progressive censored samples is different from the classical full sample case. The aim of this study is to estimate the shape parameter of the Weibull distribution based on the progressive censored sample. For this purpose, the shape parameter of the Weibull distribution was estimated using a simple linear regression model. Least Squares (OLS) and robust estimation method M (Huber, Tukey and Hampel) estimators are used as estimation method. The efficiencies of these estimation methods were compared with the Monte-Carlo simulation study according to whether the data set contains outliers or not. As a result, M estimators was determined as the most effective estimators for the estimation of the shape parameter of the Weibull distribution based on the progressive censored sample.

Keywords

• Statistics
• Reliability analysis
• Weibull distribution
• Prograssive censored sample
• Robust estimator

İlerleyen Sansürlü Örneklemlere Dayalı Olarak Weibull Dağılımının Şekil Parametresinin Sağlam Tahmin Edicileri

Abstract

Yaşam modellerinde parametre tahmini oldukça önemli bir konudur. Uygulamada karşılaşılan veri tipi genellikle ilerleyen sansürlenmiş veri şeklindedir. İlerleyen sansürlü örneklemlere dayalı parametre tahmini, klasik tam örneklem durumundan farklıdır. Bu çalışmanın amacı ilerleyen sansürlü veriye dayalı olarak Weibull dağılımının şekil parametresini tahmin etmektir. Bu amaçla Weibull dağılımının şekil parametresi basit doğrusal regresyon modeli kullanılarak tahmin edilmiştir. Tahmin yöntemi olarak En Küçük Kareler (EKK) ve sağlam (robust) tahmin yöntemi olan M (Huber, Tukey ve Hampel) tahmin edicileri ele alınmıştır. Bu tahmin yöntemlerinin etkinlikleri veri setinin aykırı değer içerip içermeme durumuna göre Monte-Carlo simülasyon çalışmasıyla karşılaştırılmıştır. Sonuç olarak, ilerleyen sansürlü örnekleme dayalı olarak Weibull dağılımının şekil parametresinin tahmini için en etkili tahmin edicinin M tahmin ediciler olduğu belirlenmiştir.

Keywords

• İstatistik
• Güvenilirlik analizi
• Weibull dağılımı
• İlerleyen sansürlü örneklem
• Sağlam tahmin edici

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