Inverted Modified Lindley Dağılımı için Parametre Tahmin Yöntemlerinin Karşılaştırılması

Öz

Inverted Modified Lindley (IML) dağılımının, üstel ve Lindley dağılımlarına kıyasla daha iyi uyum sağlama yetenekleri gösterdiği önceki çalışmalarala gösterilmiştir. Bu çalışma, En Küçük Kareler (LS), Cramer von Misses (CvM) ve Maksimum Olabilirlik (ML) yöntemlerini kullanarak Inverted Modified Lindley (IML) dağılımının parametre tahminini incelemektedir. IML dağılımına ait parametrenin tahmin edilmesinde ML, LS ve CvM yöntemlerinin etkinliğini karşılaştırmak amacıyla bir Monte Carlo simülasyon çalışması yapılmıştır. Ayrıca ilgili tahmin yöntemleri kullanılarak çeşitli alanlardan gerçek veri uygulamaları sağlanmıştır. Bu yöntemlerin uyum performansı, ortalama karekök hata, belirleme katsayısı ve Kolmogorov-Smirnov testi kullanılarak değerlendirilmiştir. Uygulama sonuçlarına göre CvM metodu, IML dağılımı için dikkate alınan verileri daha bir iyi şekilde tanımlarken, simülasyon çalışması için ise, ML tahmin yöntemi öne çıkmaktadır.

Anahtar Kelimeler

• Cramer von Missess
• En küçük kareler
• En çok olabilirlik
• Inverted Modified Lindley

A Comparison of Parameter Estimation Methods for the Inverted Modified Lindley Distribution

Öz

The Inverted Modified Lindley (IML) distribution has been shown to exhibit superior fitting capabilities compared to the exponential and Lindley distributions. This study investigates the parameter estimation of the IML distribution using the Least Squares (LS), Cramer von Misses (CvM), and Maximum Likelihood (ML) methods. A Monte Carlo simulation study is conducted to compare the efficiency of the ML, LS, and CvM methods in estimating the parameters of the IML distribution. Moreover, real data applications from various fields are provided using related estimation methods. The fitting performance of these methods is evaluated using root mean squared error, coefficient of determination, and the Kolmogorov-Smirnov test. According to the application results, the CvM estimates describe the considered data for the IML distribution best, while the simulation study favors ML estimation among the considered methods.

Anahtar Kelimeler

• Cramer von Missess
• Estimation
• Inverted Modified Lindley
• Least Squares
• Maximum Likelihood

Kaynakça

1. Abd Al-Fattah, A. M., El-Helbawy, A. A., & Al-Dayian, G. R. (2017). Inverted Kumaraswamy distribution: properties and estimation. Pakistan Journal of Statistics, 33(1).
2. Abouammoh, A. M., & Alshingiti, A. M. (2009). Reliability estimation of generalized inverted exponential distribution. Journal of Statistical Computation and Simulation, 79(11), 1301–1315. https://doi.org/10.1080/00949650802261095
3. Arslan, T., Acitas, S., & Senoglu, B. (2022). Modified minimum distance estimators: definition, properties and applications. Computational Statistics, 37(4), 1551–1568. https://doi.org/10.1007/s00180-021-01170-8
4. Bagci, K., Arslan, T., & Celik, H. E. (2021). Inverted Kumarswamy distribution for modeling the wind speed data: Lake Van, Turkey. Renewable and Sustainable Energy Reviews, 135, 110110. https://doi.org/https://doi.org/10.1016/j.rser.2020.110110
5. Bagci, K., Erdogan, N., Arslan, T., & Celik, H. E. (2022). Alpha power inverted Kumaraswamy distribution: Definition, different estimation methods, and application. Pakistan Journal of Statistics and Operation Research, 13–25.
6. Bhaumik, D. K., & Gibbons, R. D. (2006). One-sided approximate prediction intervals for at least p of m observations from a gamma population at each of r locations. Technometrics, 48(1), 112–119. https://doi.org/10.1198/004017005000000355
7. Chesneau, C., Tomy, L., Gillariose, J., & Jamal, F. (2020). The inverted modified Lindley distribution. Journal of Statistical Theory and Practice, 14(3), 46. https://doi.org/10.1007/s42519-020-00116-5
8. Dey, S., Singh, S., Tripathi, Y. M., & Asgharzadeh, A. (2016). Estimation and prediction for a progressively censored generalized inverted exponential distribution. Statistical Methodology, 32, 185–202. https://doi.org/https://doi.org/10.1016/j.stamet.2016.05.007

9. Donoho, D. L., & Liu, R. C. (1988). The" automatic" robustness of minimum distance functionals. The Annals of Statistics, 16(2), 552–586.
10. Hasaballah, M. M., Tashkandy, Y. A., Bakr, M. E., Balogun, O. S., & Ramadan, D. A. (2024). Classical and Bayesian inference of inverted modified Lindley distribution based on progressive type-II censoring for modeling engineering data. AIP Advances, 14(3), 035021. https://doi.org/10.1063/5.0190542
11. Hassan, A. S., Elgarhy, M., & Ragab, R. (2020). Statistical properties and estimation of inverted Topp-Leone distribution. J. Stat. Appl. Probab, 9(2), 319–331.
12. Khan, M. S. (2014). Modified inverse Rayleigh distribution. International Journal of Computer Applications, 87(13), 28–33.
13. Kumar, D., Nassar, M., Dey, S., Elshahhat, A., & Diyali, B. (2022). Analysis of an inverted modified Lindley distribution using dual generalized order statistics. Strength of Materials, 54(5), 889–904. https://doi.org/10.1007/s11223-022-00466-4
14. Kumar, D., Yadav, P., & Kumar, J. (2023). Classical inferences of order statistics for inverted modified Lindley distribution with applications. Strength of Materials, 55(2), 441–455. https://doi.org/10.1007/s11223-023-00537-0
15. Murthy, D. N. P., Xie, M., & Jiang, R. (2004). Weibull models. John Wiley & Sons.
16. Rasekhi, M., Alizadeh, M., Altun, E., Hamedani, G. G., Afify, A. Z., & Ahmad, M. (2017). The modified exponential distribution with applications. Pakistan Journal of Statistics, 33(5).
17. Sharma, V. K., Singh, S. K., Singh, U., & Agiwal, V. (2015). The inverse Lindley distribution: a stress-strength reliability model with application to head and neck cancer data. Journal of Industrial and Production Engineering, 32(3), 162–173. https://doi.org/10.1080/21681015.2015.1025901