Üstel Yarı Lojistik Dağılımın Parametreleri İçin İstatistiksel Sonuç Çıkarım

Öz

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.

Anahtar Kelimeler

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

Inference for the Parameters of the Exponentiated Half Logistic Distribution

Öz

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.

Anahtar Kelimeler

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

Destekleyen Kurum

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

Etik Beyan

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

Kaynakça

1. Kang, S. B., & Seo, J. I. (2011). Estimation in an Exponentiated Half Logistic Distribution under Progressively Type-II Censoring. Communications for Statistical Applications and Methods, 18(5), 657-666. https://doi.org/10.5351/CKSS.2011.18.5.657
2. Xiong, Z., & Gui, W. (2021). Classical and Bayesian Inference of an Exponentiated Half-Logistic Distribution under Adaptive Type II Progressive Censoring. Entropy, 23(12), 1558. https://doi.org/10.3390/e23121558
3. Kim, Y., Kang, S. B., and Seo, J. I. (2011). Bayesian estimations on the exponentiated distribution family with type-II right censoring. Communications of the Korean Statistical Society, 18, 603-613.
4. Kang, S. B., Seo, J. I., & Kim, Y. (2013). Bayesian analysis of an exponentiated half-logistic distribution under progressively type-II censoring. Journal of the Korean Data and Information Science Society, 24(6), 1455-1464. https://doi.org/10.7465/jkdi.2013.24.6.1455
5. Seo, J. I., & Kang, S. B. (2015). Notes on the exponentiated half logistic distribution. Applied Mathematical Modelling, 39(21), 6491-6500. https://doi.org/10.1016/j.apm.2015.01.039
6. Seo, J. I., & Kang, S. B. (2016). More efficient approaches to the exponentiated half-logistic distribution based on record values. SpringerPlus, 5(1), 1433. https://doi.org/10.1186/s40064-016-3047-y
7. Gui, W. (2017). Exponentiated half logistic distribution: Different estimation methods and joint confidence regions. Communications in Statistics - Simulation and Computation, 46(6), 4600-4617. https://doi.org/10.1080/03610918.2015.1122053
8. Rao, G. S. (2018). A Control Chart for Time Truncated Life Tests Using Exponentiated Half Logistic Distribution. Applied Mathematics & Information Sciences, 12(1), 125-131. https://doi.org/10.18576/amis/120111

9. Rao, G.S., Rosaiah, K., & Naidu, Ch. R. (2020). Design of multiple-deferred state sampling plans for exponentiated half logistic distribution. Cogent Mathematics & Statistics, 7(1), 1857915. https://doi.org/10.1080/25742558.2020.1857915
10. Alotaibi, R. M., Rezk, H. R., Ghosh, I., & Dey, S. (2021). Bivariate exponentiated half logistic distribution: Properties and application. Communications in Statistics - Theory and Methods, 50(24), 6099-6121. https://doi.org/10.1080/03610926.2020.1739310
11. Rao, G.S., Rosaiah, K., & Naidu, Ch. R. (2023). Multiple dependent state repetitive sampling plans for exponentiated half logistic distribution. International Journal of Management Science and Engineering Management, 18(2), 118-125. https://doi.org/10.1080/17509653.2021.2024097
12. Hassan, A. S., & Morgan, Y. S. (2025). Stress-strength reliability inference for exponentiated half-logistic distribution containing outliers. Quality & Quantity, 59(1), 275-311. https://doi.org/10.1007/s11135-024-01927-5
13. Swain, J. J., Venkatraman, S., & Wilson, J. R. (1988). Least-squares estimation of distribution functions in Johnson's translation system. Journal of Statistical Computation and Simulation, 29(4), 271-297.
14. Akgül, F. G. (2018). Comparison of the Estimation Methods for the Parameters of Exponentiated Reduced Kies Distribution. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22(3), 1209-1216. https://doi.org/10.19113/sdufenbed.498870
15. Kantar, Y. M., & Şenoğlu, B. (2008). A comparative study for the location and scale parameters of the Weibull distribution with given shape parameter. Computers & Geosciences, 34(12), 1900-1909.
16. Wolfowitz, J. (1953). Estimation by the minimum distance method. Annals of the institute of Statistical Mathematics, 5(1), 9-23.
17. Wolfowitz, J. (1957). The minimum distance method. The Annals of Mathematical Statistics, 75-88.
18. Gemeay, A. M., Sapkota, L. P., Tashkandy, Y. A., Bakr, M. E., Balogun, O. S., & Hussam, E. (2024). New bounded probability model: Properties, estimation, and applications. Heliyon, 10(23).
19. Alsadat, N., Taniş, C., Sapkota, L. P., C.S., R., Bahloul, M. M., & Gemeay, A. M. (2024). Power unit exponential probability distribution: Statistical inference and applications. Alexandria Engineering Journal, 107, 332-346. https://doi.org/10.1016/j.aej.2024.07.038
20. Cheng, R. C. H., & Amin, N. A. K. (1983). Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society: Series B (Methodological), 45(3), 394-403.
21. Kao, J. H. K. (1958). Computer methods for estimating Weibull parameters in reliability studies. IRE Transactions on Reliability and Quality Control. PG-RQC-03: 15–22.
22. Torabi, H. (2008). A general method for estimating and hypotheses testing using spacings. Journal of Statistical Theory and Applications, 8(2), 163–168.
23. Nasa Power. https://power.larc.nasa.gov/data-access-viewer/
24. Akgül, F. G., & Şenoğlu, B. (2023). Comparison of wind speed distributions: a case study for Aegean coast of Turkey. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 45(1), 2453-2470.