A COMPARISON OF DIFFERENT ESTIMATION METHODS FOR THE PARAMETERS OF THE WEIBULL LINDLEY DISTRIBUTION

Yıl 2020, , 19 - 33, 28.02.2020

Şükrü Acıtaş , Talha Arslan

https://doi.org/10.20290/estubtdb.529328

Öz

In this study, we consider different estimation methods for the parameters of Weibull Lindley distribution introduced by Ashgarzadeh et al. [1].  We consider maximum likelihood (ML), least squares (LS), weighted least squares (WLS), Cramer Von Mises (CVM) and Anderson Darling (AD) estimation methods. The main focus of this study is to examine performances of these estimation methods. For this purpose, we carry out a Monte-Carlo simulation study based on different parameter settings and various values of the sample size. Results show that LS and CVM estimators are more preferable. Two real life data sets are also taken into account at end of the study. 

Anahtar Kelimeler

Weibull Lindley distribution, Parameter estimation, Bias, Efficiency

WEIBULL LINDLEY DAĞILIMININ PARAMETRELERİ İÇİN FARKLI TAHMİN YÖNTEMLERİNİN KARŞILAŞTIRILMASI

Öz

Bu çalışmada,  Ashgarzadeh ve ark. [1] tarafından önerilen Weibull Lindley dağılımının parametreleri için farklı tahmin yöntemleri ele alınmıştır. En çok olabilirlik (ML), ek küçük kareler (LS), ağırlıklandırılmış en küçük kareler (WLS), Cramer Von Mises (CVM) ve Anderson Darling (AD) yöntemleri ele alınmıştır. Bu çalışmanın ana amacı, bu tahmin yöntemlerinin performanslarının karşılaştırılmasıdır. Bu amaçla, farklı parametre değerlerine ve örnek hacmi değerlerine dayalı Monte-Carlo simülasyon çalışması yapılmıştır. Sonuçlari LS ve CVM yöntemlerinin daha tercih edilebilir olduğunu göstermiştir. Çalışmanın sonunda iki gerçek yaşam verisi ele alınmıştır. 

Anahtar Kelimeler

Weibull Lindley dağılımı, Parametre Tahmini, Yan, Etkinlik

Kaynakça

• Asgharzadeh, A. K. B. A. R., Nadarajah, S., & Sharafi, F. 2018. Weibull Lindley distribution. REVSTAT-Statistical Journal, 16(1), 87-113.
• Lindley, D. V. 1958. Fiducial distributions and Bayes' theorem. Journal of the Royal Statistical Society. Series B (Methodological), 102-107.
• Ghitany, M. E., Atieh, B., & Nadarajah, S. 2008. Lindley distribution and its application. Mathematics and computers in simulation, 78(4), 493-506.
• Nadarajah, S., Bakouch, H. S., & Tahmasbi, R. 2011. A generalized Lindley distribution. Sankhya B, 73(2), 331-359.
• Oluyede, B. O., & Yang, T. 2015. A new class of generalized Lindley distributions with applications. Journal of Statistical Computation and Simulation, 85(10), 2072-2100.
• Ghitany, M. E., Alqallaf, F., Al-Mutairi, D. K., & Husain, H. A. 2011. A two-parameter weighted Lindley distribution and its applications to survival data. Mathematics and Computers in simulation, 81(6), 1190-1201.
• Bakouch, H. S., Al-Zahrani, B. M., Al-Shomrani, A. A., Marchi, V. A., & Louzada, F. 2012. An extended Lindley distribution. Journal of the Korean Statistical Society, 41(1), 75-85.
• Ghitany, M. E., Al-Mutairi, D. K., Balakrishnan, N., & Al-Enezi, L. J. 2013. Power Lindley distribution and associated inference. Computational Statistics & Data Analysis, 64, 20-33.
• Kantar, Y.M., Senoglu, 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.
• Akgul, F.G., Senoglu, B. and Arslan, T. 2016. An alternative distribution to Weibull for modeling the wind speed data: Inverse Weibull distribution. Energy Conversion and Management, 114, 234-240.
• Akgul, F.G. 2018. Comparison of the Estimation Methods for the Parameters of Exponentiated Reduced Kies Distribution. Süleyman Demirel University Journal of Natural and Applied Sciences 22(3), 1209-1216.
• Mudholkar, G. S., Srivastava, D. K., & Freimer, M. 1995. The exponentiated Weibull family: A reanalysis of the bus-motor-failure data. Technometrics, 37(4), 436-445.
• Xie, M., Tang, Y., & Goh, T. N. 2002. A modified Weibull extension with bathtub-shaped failure rate function. Reliability Engineering & System Safety, 76(3), 279-285.
• Lai, C. D., Xie, M., & Murthy, D. N. P. 2003. A modified Weibull distribution. IEEE Transactions on reliability, 52(1), 33-37.
• Carrasco, J. M., Ortega, E. M., & Cordeiro, G. M. 2008. A generalized modified Weibull distribution for lifetime modeling. Computational Statistics & Data Analysis, 53(2), 450-462.
• Cordeiro, G. M., Gomes, A. E., da-Silva, C. Q., & Ortega, E. M. 2013. The beta exponentiated Weibull distribution. Journal of Statistical Computation and Simulation, 83(1), 114-138.
• Lai, C. D. 2014. Generalized Weibull Distributions (pp. 23-75). Springer, Berlin, Heidelberg.
• Mazucheli, J., Louzada, F., & Ghitany, M. E. 2013. Comparison of estimation methods for the parameters of the weighted Lindley distribution. Applied Mathematics and Computation, 220, 463-471.
• Akgul, F. G., & Senoglu, B. 2018. Comparison of Estimation Methods for Inverse Weibull Distribution. In Trends and Perspectives in Linear Statistical Inference (pp. 1-22). Springer, Cham.
• Swain, J., Venkatraman, S., Wilson, J. 1988. Least squares estimation of distribution function in Johnson’s translation system. Journal of Statistical Computation and Simulation, 29, 271–297.
• Duchesne, T., Rioux, J. and Luong, A. 1997. Minimum Cramer-von Mises estimators and their influence function, Actuarial Research Clearing House, 1, 349-361.
• Boos, D.D. 1981. Minimum distance estimators for location and goodness of fit. Journal of the American Statistical Association, 76, 663–670.
• Klein, J.P. and Moeschberger, M.L. (1997). Survival Analysis Techniques for Censored and Truncated Data. Springer Verlag, New York.