DUS Inverse Weibull Distribution and Parameter Estimation in Regression Model

Year 2023, Volume: 27 Issue: 1, 42 - 50, 25.04.2023

Hasan Hüseyin Gül , Şükrü Acıtaş , Hülya Bayrak , Birdal Şenoğlu

https://doi.org/10.19113/sdufenbed.1107862

Cited By: 1

Abstract

This paper considers various estimation methods to estimate the unknown parameters of the DUS Inverse Weibull (DIW) distribution using the maximum likelihood (ML), least squares (LS), weighted least squares (WLS), Cramer-von Mises (CVM) and the Anderson-Darling (AD) estimators. A Monte-Carlo simulation study is conducted to determine the most preferable estimators in terms of their efficiencies. Furthermore, the distribution of the error terms in the simple linear regression is assumed to be DIW to show the implementation of it to the linear models. We also carry out a simulation study for comparing the performances of the estimators of the unknown regression parameters.

Keywords

DUS transformation, Inverse Weibull, Parameter estimation, Lineer regression, Monte-Carlo simulation

DUS Inverse Weibull Dağılımı ve Lineer Regresyonda Parametre Tahmini

Abstract

Bu çalışma, en çok olabilirlik (ML), en küçük kareler (LS), ağırlıklı en küçük kareler (WLS), Cramer-von Mises (CM) ve Anderson-Darling (AD) tahmin edicilerini kullanarak DUS Inverse Weibull (DIW) dağılımının bilinmeyen parametrelerini tahmin etmek için çeşitli tahmin yöntemlerini ele almaktadır. Etkinlikleri açısından en çok tercih edilen tahmin edicileri belirlemek için bir Monte-Carlo simülasyon çalışması yapılmıştır. Ayrıca, lineer modellere uygulanışını göstermek için basit lineer regresyonda hata terimlerinin dağılımının DIW olduğu varsayılmıştır. Bilinmeyen regresyon parametrelerinin tahmin edicilerinin performanslarının karşılaştırılması için de bir simülasyon çalışması yapılmıştır.

Keywords

DUS dönüşümü, Inverse Weibull, Parametre tahmini, Lineer regresyon, Monte-Carlo simülasyonu

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