Üstel Yarı Lojistik Dağılımın Parametreleri İçin İstatistiksel Sonuç Çıkarım

Abstract

Bu çalışma, Üstel Yarı-Lojistik dağılımının parametrelerinin on bir farklı tahmin yöntemiyle belirlenmesine odaklanmaktadır. Kullanılan yöntemler arasında en çok olabilirlik, en küçük kareler, ağırlıklı en küçük kareler, Cramér–von Mises ve çeşitli Anderson–Darling istatistikleri (standart, sağ kuyruk, sol kuyruk ve ikinci mertebeden sol kuyruk), maksimum aralık çarpımı, minimum aralık mutlak uzaklığı ve minimum aralık logaritmik mutlak uzaklığı tahmin edicileri yer almaktadır. Bu yöntemlerin farklı parametre değerleri ve örneklem büyüklükleri altında gösterdiği performanslar, kapsamlı bir Monte Carlo benzetimi ile değerlendirilmiş ve karşılaştırılmıştır. Önerilen tahmin yöntemlerinin pratik uygulanabilirliğini göstermek amacıyla, üstelleştirilmiş yarı lojistik dağılım gerçek bir rüzgâr hızı veri setine uygulanmıştır. Elde edilen sonuçlar, bu dağılımın söz konusu veri türü için yaygın olarak kullanılan modellere kıyasla daha iyi bir uyum sağladığını ortaya koymaktadır.

Keywords

• Üstel yarı lojistik dağılım
• parametre tahmini
• Monte-Carlo benzetimi
• model değerlendirmesi
• rüzgar hızı

Inference for the Parameters of the Exponentiated Half Logistic Distribution

Abstract

This study focuses on estimating the parameters of the Exponentiated Half-Logistic distribution through eleven distinct estimation techniques. These include maximum likelihood, least squares, weighted least squares, Cramér–von Mises, various forms of the Anderson–Darling method (standard, right-tailed, left-tailed, and second-order left-tailed), maximum product of spacings, minimum spacing absolute distance, and minimum spacing absolute-log distance estimators. A comprehensive Monte Carlo simulation is conducted to assess and compare the performance of these methods under varying parameter configurations and sample sizes. To illustrate the practical applicability of the proposed estimators, the corresponding distribution is fitted to a real-world wind speed data set. The results indicate that the exponentiated half logistic distribution provides a better fit than several commonly used models for this type of data.

Keywords

• Exponentiated half logistic distribution
• parameter estimation
• Monte-Carlo simulation
• model evaluation
• wind speed

Supporting Institution

The authors have no received any financial support for the research, authorship, or publication of this study.

Ethical Statement

The study does not require ethics committee permission or any special permission.

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