Comparison of the Estimation Methods for the Parameters of Exponentiated Reduced Kies Distribution

Year 2018, Volume: 22 Issue: 3, 1209 - 1216, 20.09.2018

Fatma Gül Akgül

https://doi.org/10.19113/sdufenbed.498870

Cited By: 2

Abstract

In this paper, we consider the estimation for the
parameters of exponentiated reduced Kies (ERK) distribution using maximum
likelihood (ML), least squares (LS), weighted least squares (WLS), Cramér-von
Mises (CM), Anderson Darling (AD) and right-tail Anderson Darling (RAD)
methods. The performances of the estimators are compared via Monte-Carlo
simulation study for different parameter settings and different sample sizes.
Finally, a real data set is analyzed for the implementation of the proposed
methods.

Keywords

Exponentiated reduced Kies distribution;, Parameter estimation;, Monte-Carlo simulation;, Efficiency

Exponentiated Reduced Kies Dağılımının Parametreleri için Tahmin Yöntemlerinin Karşılaştırılması

Abstract

Bu
makalede, exponentiated reduced Kies (ERK) dağılımının parametreleri en çok
olabilirlik, en küçük kareler, ağırlıklandırılmış en küçük karaler, Cramér-von
Mises, Anderson Darling ve sağ-kuyruklu Anderson Darling yöntemleri
kullanılarak tahmin edilmiştir. Tahmin edicilerin performansları farklı
parametre değerleri ve farklı örneklemler boyutları için Monte-Carlo simülasyon
çalışması ile karşılaştırılmıştır. Son olarak, önerilen yöntemlerin uygulanması
için gerçek bir veri seti analiz edilmiştir.

Keywords

Exponentiated reduced Kies dağılımı, Parametre tahmini, Monte-Carlo simülasyonu, Etkinlik

References

• [1] Kantar, Y. M., Şenoğlu, B. 2008. A comparative study for the location and scale parameters of the Weibull distribution with given shape parameter. Computer and Geosciences, 34, 1900-1909.
• [2] Akgül, F. G., Şenoğlu, B., Arslan, T. 2016. An alternative distribution to Weibull for modeling the wind speed data: Inverse Weibull distribution. Energy Conversion and Management, 114, 234-240.
• [3] Mudholkar, G. S., Srivastava, D. K. 1993. Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability, 42, 299-302.
• [4] Mudholkar, G. S., Kollia, G. D. 1994. Generalized Weibull family: a structural analysis. Communications in Statistics – Theory and Methods, 23(4), 1149-71.
• [5] Xie, M., Tang, Y., Goh, T. N. 2002. A modified Weibull extension with bathtub-shaped failure rate function. Reliability Engineering and System Safety, 76, 279-285.
• [6] Lee, C., Famoye, F., Olumolade, O. 2007. Beta-Weibull distribution: Some properties and applications to censored data. Journal of Modern Applied Statistical Methods, 6(1), 173-186.
• [7] Cordeiro, G. M., Gomes, A. E., Queiroz da-Silva, C., Ortega, E. M. M. 2013. The beta exponentiated Weibull distribution. Journal of Statistical Computation and Simulation, 83(1), 114-138.
• [8] Kies, J. A. 1958. The strength of glass performance. Naval Research Lab Report No. 5093, Washington, D.C.
• [9] Kumar, C. S., Dharmaja, S. H. S. 2014. On some properties of Kies distribution. Metron, 72, 97-122.
• [10] Kumar, C. S., Dharmaja, S. H. S. 2013. On reduced Kies distribution. In: Kumar, C.S., Chacko, M., Sathar, E.I.A., eds. Collection of Recent Statistical Methods and Applications, (pp. 111–123). Trivandrum: Department of Statistics, University of Kerala Publishers.
• [11] Kumar, C. S., Dharmaja, S. H. S. 2017. The exponentiated reduced Kies distribution: Properties and applications. Communications in Statistics – Theory and Methods, 46(17), 8778-90.
• [12] Wolfowitz, J. 1953. Estimation by the minimum distance methods. Ann. Ins. Stat. Math. 5, 9-23.
• [13] Wolfowitz, J. 1957. The minimum distance methods. Ann. Math. Stat. 28, 75-88.
• [14] Luceño, A. 2008. Maximum likelihood vs. maximum goodness of fit estimation of the three-parameter Weibull distribution. Journal of Statistical Computation and Simulation, 78(10), 941-949.
• [15] Santo, A. P. J. E., Mazucheli, J. 2015. Comparison of estimation methods for the Marshall-Olkin extended Lindley distribution. Journal of Statistical Computation and Simulation, 85(17), 3437-3450.
• [16] Mazucheli, J., Ghitany, M. E., Louzada, F. 2017. Comparisons of ten estimation methods for the parameters of Marshall-Olkin extended exponential distribution. Communications in Statistics – Simulation and Computation, 46(7), 5627-5645.
• [17] Akgül, F. G., Şenoğlu, B. 2018. Comparison of Estimation Methods for Inverse Weibull Distribution. 1-22. Tez, M., von Rosen, D. 2018. Trends and Perspectives in Linear Statistical Inference, Springer.
• [18] Wingo, D. R. 1983. Maximum likelihood methods for fitting the Burr XII distribution to life test data. Biom J., 25, 77-84.