Estimating the Parameters of Xgamma Weibull Distribution

Abstract

In this paper, we consider a comparison of estimation methods for the parameters of Xgamma Weibull distribution. It is discussed five different estimation methods such as maximum likelihood method, least-squares method, weighted least-squares method, the method of Anderson-Darling and the method of Crámer–von-Mises. We compare these estimators via Monte Carlo simulations according to the biases and mean-squared errors (MSEs). Further, seven real data applications are conducted and Kolmogorov Smirnov goodness of fit test is also calculated for all estimators.

Keywords

• Xgamma Weibull distribution
• Maximum likelihood method
• Least-squares method
• Weighted least-squares method
• Anderson-Darling method
• Crámer–von-Mises estimation method

Xgamma Weibull Dağılımının Parametre Tahmini

Abstract

Bu çalışmada, Xgamma Weibull dağılımının parametre tahmini için tahmin yöntemlerinin kıyaslanması problemi ele alınmıştır. En çok olabilirlik yöntemi, en küçük kareler yöntemi, ağırlıklandırılmış en küçük kareler yöntemi, Anderson-Darling yöntemi ve Crámer–von-Mises yöntemi olmak üzere beş tahmin yöntemi incelenmiştir. Bu beş tahmin yöntemini yan ve hata kareler ortalaması açısından karşılaştırabilmek için bir Monte Carlo simülasyon çalışması yapılmıştır. Ayrıca yedi gerçek veri uygulaması yapılmış ve tüm tahmin ediciler için Kolmogorov Smirnov uyum iyiliği testi hesaplanmıştır.

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