Unit-Weibull Distribution: Different Method of Estimations

Year 2023, Volume: 13 Issue: 2, 547 - 560, 15.06.2023

Hasan Hüseyin Gül

https://doi.org/10.31466/kfbd.1239446

Abstract

Recently, the unit-Weibull (UW) distribution is used quite effectively in analyzing lifetime data. The main goal of this article is to investigate the performance of seven estimation methods, namely maximum likelihood (ML), least square (LS), weighted least square (WLS), Anderson-Darling (AD), right-tail Anderson-Darling (RAD), Cramer-von-Mises (CVM) and percentile (PCE) for parameter estimation. An extensive Monte Carlo simulation study is considered to compare the performances of these methods through biases and mean square errors (MSEs). The numerical results show that the PCE estimator has significantly smaller MSE value for different sample sizes and parameter values in most cases. In addition, the ML and LS estimators have lower bias values than the other estimators in general. Finally, a real data set is presented for illustrative purposes.

Keywords

Unit-Weibull distribution, Estimation methods, Maximum likelihood, Anderson-Darling, Least square

Unit-Weibull Dağılımı: Tahmin Metotları

Abstract

Son zamanlarda Unit-Weibull (UW) dağılımı yaşam zamanı verilerin analizinde oldukça etkin bir şekilde kullanılmaktadır. Bu makalenin temel amacı, en çok olabilirlik (ML), en küçük kareler (LS), ağırlıklı en küçük kareler (WLS), Anderson-Darling (AD), sağ kuyruklu Anderson-Darling (RAD), Cramer-von-Mises (CVM) and percentile (PCE) olmak üzere yedi tahmin yönteminin performansını karşılaştırmaktır. Bu yöntemlerin performanslarını yan ve hata kare ortalaması (MSE'ler) aracılığıyla karşılaştırmak için kapsamlı bir Monte Carlo simülasyon çalışması düşünülmüştür. Sayısal sonuçlar, PCE tahmin edicisinin çoğu durumda farklı örneklem büyüklükleri ve parametre değerleri için önemli ölçüde daha küçük MSE değerine sahip olduğunu göstermektedir. Ayrıca ML ve LS tahmin edicileri genel olarak diğer tahmin edicilere göre daha düşük yan değerlerine sahiptir. Son olarak, açıklama amacıyla gerçek bir veri seti sunulmuştur.

Keywords

Unit-Weibull dağılımı, En çok olabilirlik, Anderson-Darling, En küçük kareler

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