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Estimating the Parameters of Xgamma Weibull Distribution

Year 2020, Volume: 10 Issue: 2, 557 - 571, 30.12.2020
https://doi.org/10.37094/adyujsci.781069

Abstract

In this paper, we consider a comparison of estimation methods for the parameters of Xgamma Weibull distribution. It is discussed five different estimation methods such as maximum likelihood method, least-squares method, weighted least-squares method, the method of Anderson-Darling and the method of Crámer–von-Mises. We compare these estimators via Monte Carlo simulations according to the biases and mean-squared errors (MSEs). Further, seven real data applications are conducted and Kolmogorov Smirnov goodness of fit test is also calculated for all estimators.

References

  • [1] Yousof, H.M., Korkmaz, M.Ç., Sen, S., A new two-parameter lifetime model, Annals of Data Science, 2020, DOI: 10.1007/s40745-019-00203-w.
  • [2] Gupta, R.D., Kundu, D., Generalized exponential distribution: different method of estimations, Journal of Statistical Computation and Simulation, 69(4), 315-337, 2001.
  • [3] Kundu, D., Raqab, M.Z., Generalized Rayleigh distribution: different methods of estimations, Computational statistics & data analysis, 49(1), 187-200, 2005.
  • [4] Asgharzadeh, A., Rezaie, R., Abdi, M., Comparisons of methods of estimation for the half-logistic distribution, Selçuk Journal of Applied Mathematics, 93-108, 2011.
  • [5] Mazucheli, J., Louzada F., Ghitany M.E., Comparison of estimation methods for the parameters of the weighted Lindley distribution, Applied Mathematics and Computation, 220, 463-471, 2013.
  • [6] Dey, S., Dey, T., Kundu, D., Two-parameter Rayleigh distribution: different methods of estimation, American Journal of Mathematical and Management Sciences, 33(1), 55-74, 2014.
  • [7] Peng, X., Yan, Z., Estimation and application for a new extended Weibull distribution, Reliability Engineering & System Safety, 121, 34-42, 2014.
  • [8] Nassar, M., Afify, A.Z., Dey, S., Kumar, D., A new extension of Weibull distribution: properties and different methods of estimation, Journal of Computational and Applied Mathematics, 336, 439-457, 2018.
  • [9] Taniş, C., Saracoglu, B., Comparisons of six different estimation methods for log- kumaraswamy distribution, Thermal Science, 23, 1839-1847, 2019.
  • [10] Afify, A.Z., Nassar, M., Cordeiro, G. M., Kumar, D., The Weibull Marshall–Olkin Lindley distribution: properties and estimation, Journal of Taibah University for Science, 14(1), 192-204, 2020.
  • [11] Feigl, P., Zelen, M., Estimation of exponential survival probabilities with concomitant information, Biometrics 21, 826–38, 1965.
  • [12] Nichols, M.D., Padgett, W.J., A bootstrap control chart for Weibull percentiles, Quality and Reliability Engineering International, 22, 141-151, 2006.
  • [13] Lawless, J.F., Statistical models and methods for lifetime data, Wiley, New York, 2003.
  • [14] Bjerkedal, T., Acquisition of resistance in Guinea Piesinfected with different doses of Virulent Tubercle Bacill, American Journal of Hygiene, 72, 130-148 , 1960.
  • [15] Lee, E.T., Statistical methods for survival data analysis, John Wiley, New York, 1992. [16] Xu, K., Xie, M., Tang, L.C., Ho, S.L., Application of neural networks in forecasting engine systems reliability, Applied Soft Computing, 2(4), 255-268, 2003.
  • [16] Xu, K., Xie, M., Tang, L.C., Ho, S.L., Application of neural networks in forecasting engine systems reliability, Applied Soft Computing, 2(4), 255-268, 2003.
  • [17] Crowder, M.J., Kimber, A.C., Smith, R.L., Sweeting, T.J. The statistical analysis of reliability data, Chapman and Hall, London, 1991.

Xgamma Weibull Dağılımının Parametre Tahmini

Year 2020, Volume: 10 Issue: 2, 557 - 571, 30.12.2020
https://doi.org/10.37094/adyujsci.781069

Abstract

Bu çalışmada, Xgamma Weibull dağılımının parametre tahmini için tahmin yöntemlerinin kıyaslanması problemi ele alınmıştır. En çok olabilirlik yöntemi, en küçük kareler yöntemi, ağırlıklandırılmış en küçük kareler yöntemi, Anderson-Darling yöntemi ve Crámer–von-Mises yöntemi olmak üzere beş tahmin yöntemi incelenmiştir. Bu beş tahmin yöntemini yan ve hata kareler ortalaması açısından karşılaştırabilmek için bir Monte Carlo simülasyon çalışması yapılmıştır. Ayrıca yedi gerçek veri uygulaması yapılmış ve tüm tahmin ediciler için Kolmogorov Smirnov uyum iyiliği testi hesaplanmıştır.

References

  • [1] Yousof, H.M., Korkmaz, M.Ç., Sen, S., A new two-parameter lifetime model, Annals of Data Science, 2020, DOI: 10.1007/s40745-019-00203-w.
  • [2] Gupta, R.D., Kundu, D., Generalized exponential distribution: different method of estimations, Journal of Statistical Computation and Simulation, 69(4), 315-337, 2001.
  • [3] Kundu, D., Raqab, M.Z., Generalized Rayleigh distribution: different methods of estimations, Computational statistics & data analysis, 49(1), 187-200, 2005.
  • [4] Asgharzadeh, A., Rezaie, R., Abdi, M., Comparisons of methods of estimation for the half-logistic distribution, Selçuk Journal of Applied Mathematics, 93-108, 2011.
  • [5] Mazucheli, J., Louzada F., Ghitany M.E., Comparison of estimation methods for the parameters of the weighted Lindley distribution, Applied Mathematics and Computation, 220, 463-471, 2013.
  • [6] Dey, S., Dey, T., Kundu, D., Two-parameter Rayleigh distribution: different methods of estimation, American Journal of Mathematical and Management Sciences, 33(1), 55-74, 2014.
  • [7] Peng, X., Yan, Z., Estimation and application for a new extended Weibull distribution, Reliability Engineering & System Safety, 121, 34-42, 2014.
  • [8] Nassar, M., Afify, A.Z., Dey, S., Kumar, D., A new extension of Weibull distribution: properties and different methods of estimation, Journal of Computational and Applied Mathematics, 336, 439-457, 2018.
  • [9] Taniş, C., Saracoglu, B., Comparisons of six different estimation methods for log- kumaraswamy distribution, Thermal Science, 23, 1839-1847, 2019.
  • [10] Afify, A.Z., Nassar, M., Cordeiro, G. M., Kumar, D., The Weibull Marshall–Olkin Lindley distribution: properties and estimation, Journal of Taibah University for Science, 14(1), 192-204, 2020.
  • [11] Feigl, P., Zelen, M., Estimation of exponential survival probabilities with concomitant information, Biometrics 21, 826–38, 1965.
  • [12] Nichols, M.D., Padgett, W.J., A bootstrap control chart for Weibull percentiles, Quality and Reliability Engineering International, 22, 141-151, 2006.
  • [13] Lawless, J.F., Statistical models and methods for lifetime data, Wiley, New York, 2003.
  • [14] Bjerkedal, T., Acquisition of resistance in Guinea Piesinfected with different doses of Virulent Tubercle Bacill, American Journal of Hygiene, 72, 130-148 , 1960.
  • [15] Lee, E.T., Statistical methods for survival data analysis, John Wiley, New York, 1992. [16] Xu, K., Xie, M., Tang, L.C., Ho, S.L., Application of neural networks in forecasting engine systems reliability, Applied Soft Computing, 2(4), 255-268, 2003.
  • [16] Xu, K., Xie, M., Tang, L.C., Ho, S.L., Application of neural networks in forecasting engine systems reliability, Applied Soft Computing, 2(4), 255-268, 2003.
  • [17] Crowder, M.J., Kimber, A.C., Smith, R.L., Sweeting, T.J. The statistical analysis of reliability data, Chapman and Hall, London, 1991.
There are 17 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Mathematics
Authors

Kadir Karakaya 0000-0002-0781-3587

Caner Tanış 0000-0003-0090-1661

Publication Date December 30, 2020
Submission Date August 15, 2020
Acceptance Date December 2, 2020
Published in Issue Year 2020 Volume: 10 Issue: 2

Cite

APA Karakaya, K., & Tanış, C. (2020). Estimating the Parameters of Xgamma Weibull Distribution. Adıyaman University Journal of Science, 10(2), 557-571. https://doi.org/10.37094/adyujsci.781069
AMA Karakaya K, Tanış C. Estimating the Parameters of Xgamma Weibull Distribution. ADYU J SCI. December 2020;10(2):557-571. doi:10.37094/adyujsci.781069
Chicago Karakaya, Kadir, and Caner Tanış. “Estimating the Parameters of Xgamma Weibull Distribution”. Adıyaman University Journal of Science 10, no. 2 (December 2020): 557-71. https://doi.org/10.37094/adyujsci.781069.
EndNote Karakaya K, Tanış C (December 1, 2020) Estimating the Parameters of Xgamma Weibull Distribution. Adıyaman University Journal of Science 10 2 557–571.
IEEE K. Karakaya and C. Tanış, “Estimating the Parameters of Xgamma Weibull Distribution”, ADYU J SCI, vol. 10, no. 2, pp. 557–571, 2020, doi: 10.37094/adyujsci.781069.
ISNAD Karakaya, Kadir - Tanış, Caner. “Estimating the Parameters of Xgamma Weibull Distribution”. Adıyaman University Journal of Science 10/2 (December 2020), 557-571. https://doi.org/10.37094/adyujsci.781069.
JAMA Karakaya K, Tanış C. Estimating the Parameters of Xgamma Weibull Distribution. ADYU J SCI. 2020;10:557–571.
MLA Karakaya, Kadir and Caner Tanış. “Estimating the Parameters of Xgamma Weibull Distribution”. Adıyaman University Journal of Science, vol. 10, no. 2, 2020, pp. 557-71, doi:10.37094/adyujsci.781069.
Vancouver Karakaya K, Tanış C. Estimating the Parameters of Xgamma Weibull Distribution. ADYU J SCI. 2020;10(2):557-71.

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