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

Yıl 2020, Cilt: 8 Sayı: 1, 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

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.

WEIBULL LINDLEY DAĞILIMININ PARAMETRELERİ İÇİN FARKLI TAHMİN YÖNTEMLERİNİN KARŞILAŞTIRILMASI

Yıl 2020, Cilt: 8 Sayı: 1, 19 - 33, 28.02.2020

Şükrü Acıtaş Talha Arslan

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

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.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Şükrü Acıtaş 0000-0002-4131-0086

Talha Arslan 0000-0002-4630-4857

Yayımlanma Tarihi 28 Şubat 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 8 Sayı: 1

Kaynak Göster

APA Acıtaş, Ş., & Arslan, T. (2020). A COMPARISON OF DIFFERENT ESTIMATION METHODS FOR THE PARAMETERS OF THE WEIBULL LINDLEY DISTRIBUTION. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, 8(1), 19-33. https://doi.org/10.20290/estubtdb.529328
AMA Acıtaş Ş, Arslan T. A COMPARISON OF DIFFERENT ESTIMATION METHODS FOR THE PARAMETERS OF THE WEIBULL LINDLEY DISTRIBUTION. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. Şubat 2020;8(1):19-33. doi:10.20290/estubtdb.529328
Chicago Acıtaş, Şükrü, ve Talha Arslan. “A COMPARISON OF DIFFERENT ESTIMATION METHODS FOR THE PARAMETERS OF THE WEIBULL LINDLEY DISTRIBUTION”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler 8, sy. 1 (Şubat 2020): 19-33. https://doi.org/10.20290/estubtdb.529328.
EndNote Acıtaş Ş, Arslan T (01 Şubat 2020) A COMPARISON OF DIFFERENT ESTIMATION METHODS FOR THE PARAMETERS OF THE WEIBULL LINDLEY DISTRIBUTION. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 8 1 19–33.
IEEE Ş. Acıtaş ve T. Arslan, “A COMPARISON OF DIFFERENT ESTIMATION METHODS FOR THE PARAMETERS OF THE WEIBULL LINDLEY DISTRIBUTION”, Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler, c. 8, sy. 1, ss. 19–33, 2020, doi: 10.20290/estubtdb.529328.
ISNAD Acıtaş, Şükrü - Arslan, Talha. “A COMPARISON OF DIFFERENT ESTIMATION METHODS FOR THE PARAMETERS OF THE WEIBULL LINDLEY DISTRIBUTION”. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 8/1 (Şubat 2020), 19-33. https://doi.org/10.20290/estubtdb.529328.
JAMA Acıtaş Ş, Arslan T. A COMPARISON OF DIFFERENT ESTIMATION METHODS FOR THE PARAMETERS OF THE WEIBULL LINDLEY DISTRIBUTION. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2020;8:19–33.
MLA Acıtaş, Şükrü ve Talha Arslan. “A COMPARISON OF DIFFERENT ESTIMATION METHODS FOR THE PARAMETERS OF THE WEIBULL LINDLEY DISTRIBUTION”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, c. 8, sy. 1, 2020, ss. 19-33, doi:10.20290/estubtdb.529328.
Vancouver Acıtaş Ş, Arslan T. A COMPARISON OF DIFFERENT ESTIMATION METHODS FOR THE PARAMETERS OF THE WEIBULL LINDLEY DISTRIBUTION. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2020;8(1):19-33.