A Simulation Study on Comparison of Parameter Estimation Methods for Inverse Weibull Distribution

Yıl 2025, Cilt: 15 Sayı: 3, 971 - 994, 15.09.2025

Esin Köksal Babacan

https://doi.org/10.31466/kfbd.1508353

Öz

The Inverse Weibull distribution, which is an appropriate model for analyzing lifespan data, can be used to model various characteristics such as useful life and depreciation periods. Due to its applicability in many different fields, it is important to effectively estimate the parameters of the Inverse Weibull distribution. Commonly used methods for estimating the parameters of the Inverse Weibull distribution include least squares, maximum likelihood, and Bayesian estimation methods. In the Bayesian estimation method, unlike classical approaches, parameters are also considered as random variables. Therefore, these parameters have their own distributions, known as prior distributions. These distributions are updated with sample information to obtain posterior distributions, and all inferences about the parameters are made using this posterior distribution. However, in applications, there are some challenges in calculating the posterior distribution. In such cases, numerical integration methods or simulation methods known as Markov Chain Monte Carlo methods are used to make inferences.In this study, the methods used to estimate the parameters of the Inverse Weibull distribution are examined, and these methods are compared through a simulation study. To compare the forecasting methods, mean squared error, root mean squared error, and mean absolute error metrics have been used.

Anahtar Kelimeler

Inverse Weibull distribution , bayes estimator , lindley approximation , Monte Carlo simulation

Ters Weibull Dağılımında Parametre Tahmin Yöntemlerinin Karşılaştırılması Üzerine Bir Simülasyon Çalışması

Öz

Yaşam süresi verilerini analiz etmek için uygun bir model olan Ters Weibull dağılımı, faydalı ömür ve yıpranma periyotları gibi çeşitli özellikleri modellemek için kullanılabilir. Farklı birçok alanda uygulama olanağına sahip olması nedeniyle, Ters Weibull dağılımının parametrelerinin etkin bir şekilde tahmin edilmesi önemlidir. Ters Weibull dağılımının parametrelerini tahmin etmek için genellikle; en küçük kareler, en çok olabilirlik ve Bayes tahmin yöntemleri kullanılmaktadır. Bayes tahmin yönteminde klasik yaklaşımdan farklı olarak parametreler de birer rasgele değişken olarak düşünülür. Bu nedenle parametrelerin de kendilerine ait dağılımları vardır. Önsel dağılım olarak bilinen bu dağılımlar örneklem bilgisi ile güncellenerek sonsal dağılımlar elde edilir ve parametreye ilişkin tüm çıkarımlar bu sonsal dağılım kullanılarak yapılır. Fakat uygulamalarda sonsal dağılımın hesaplanmasında bazı zorluklarla karşılaşılır. Bu gibi durumlarda sonuç çıkarımı yapabilmek için sayısal integrasyon yöntemleri veya Markov Zinciri Monte Carlo yöntemleri olarak bilinen simülasyon yöntemleri kullanılır. Bu çalışmada, Ters Weibull dağılımının parametrelerini tahmin etmek için kullanılan yöntemler incelenmiş ve yapılan simülasyon çalışması ile bu yöntemler karşılaştırılmıştır. Tahmin yöntemlerini karşılaştırmak için hata kareler ortalaması, kök hata kareler ortalaması ve ortalama mutlak hata ölçütleri kullanılmıştır.

Anahtar Kelimeler

Ters Weibull Dağılımı , Bayes Tahmin edicisi , Lindley yaklaşımı , Monte Carlo simülasyonu

Kaynakça

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