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Gompertz Flexible Weibull Dağılımı için Tahmin Yöntemlerinin bir Karşılaştırması

Year 2021, Volume: 14 Issue: 3, 887 - 897, 18.12.2021
https://doi.org/10.18185/erzifbed.777540

Abstract

Gompertz flexible Weibull dağılımı, flexible Weibull dağılımının bir türüdür. Biz Gompertz flexible Weibull dağılımının parametrelerinin tahmini problemini ele aldık. Gompertz flexible Weibull dağılımı için birkaç tahmin yöntemi üzerinde durduk. En çok olabilirlik, en küçük kareler, ağırlıklandırılmış en küçük kareler, Anderson Darling ve Cramer-von Mises tahmin edicileri düşünülmüştür. Bu tahmin edicileri yan ve hata kareler ortalaması açısından karşılaştırabilmek için bir Monte Carlo simülasyon çalışması yapılmıştır. Ayrıca Gompertz flexible Weibull dağılımının kullanışlılığını göstermek ve bahsedilen beş tahmin yöntemine dayalı olarak tahminleri elde etmek için gerçek veri çalışmaları sunulmuştur.

References

  • Ali, S., Dey, S., Tahir, M., Mansoor, M., (2020). “The Comparison Of Different Estimation Methods For The Parameters Of Flexible Weibull Distribution”, Communications Series A1 Mathematics & Statistics, 69, 794-814.
  • Asgharzadeh, A., Rezaie, R., Abdi, M., (2011). “Comparisons of methods of estimation for the half-logistic distribution”, Selçuk Journal of Applied Mathematics, 93-108.
  • Bebbington, M., Lai, C. D., Zitikis, R., (2007). “A flexible Weibull extension,” “Reliability Engineering & System Safety”, 92, 719-726.
  • Bjerkedal, T., (1960). “Acquisition of Resistance in Guinea Piesinfected with Different Doses of Virulent Tubercle Bacill”, American Journal of Hygiene, 72, 130-148.
  • Khaleel, M. A., Oguntunde,, P. E., Ahmed,, M.T., Ibrahim, N.A., Loh Y.F., (2020). “The Gompertz Flexible Weibull Distribution and its Applications,” Malaysian Journal of Mathematical Sciences, 14, 169-190.
  • Kundu, D., Raqab, M. Z., (2009). “Estimation of R = P(Y < X) for three parameter Weibull distribution”, Stat. Probab. Lett., 79, 1839–1846.
  • Kurban, M., Kanta, Y., Hocaoğlu, F. O., (2007). “Weibull Dagılımı Kullanılarak Rüzgar Hız ve Güç Yoğunluklarının İstatistiksel Analizi”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 7, 205-218.
  • Lawless, J. F., (1982). “Statistical Models and Methods for Lifetime Data”, Second ed., Wiley, New York.
  • Nassar, M., Afify, A. Z., Dey, S., Kumar, D., (2018). “A new extension of Weibull distribution: properties and different methods of estimation”, Journal of Computational and Applied Mathematics, 336, 439-457.
  • Nichols, M. D., Padgett, W. J., (2006). “A bootstrap control chart for Weibull percentiles”, Quality and Reliability Engineering International, 22, 141-151.
  • Peng X., Yan, Z., (2014). “Estimation and application for a new extended Weibull distribution,” Reliability Engineering & System Safety, 121, 34-42.
  • Taniş, C., Saracoglu, B., (2019). “Comparisons of six different estimation methods for log-Kumaraswamy distribution”, Thermal Science, 23, 1839-1847.
  • Xu, K. Xie, M., Tang, L. C., Ho, S. L., (2003). “Application of neural networks in forecasting engine systems reliability”, Applied Soft Computing, 2, 255-268.

A Comparison of Estimation Methods for Gompertz Flexible Weibull Distribution

Year 2021, Volume: 14 Issue: 3, 887 - 897, 18.12.2021
https://doi.org/10.18185/erzifbed.777540

Abstract

Gompertz flexible Weibull distribution is an extension of flexible Weibull distribution. We tackle the problem of estimation of parameters of Gompertz Weibull distribution. We discuss several methods of estimation for Gompertz flexible Weibull distribution. Maximum likelihood estimators, least squares estimators, weighted least squares estimators, Anderson-Darling estimators, Cramer-von Mises estimators are considered. A Monte Carlo simulation study is performed in order to compare these estimators in terms of their biases and mean square errors. Also, real data applications are presented to illustrate the usefulness of Gompertz flexible Weibull distribution and obtain estimates based on five methods of estimation.

References

  • Ali, S., Dey, S., Tahir, M., Mansoor, M., (2020). “The Comparison Of Different Estimation Methods For The Parameters Of Flexible Weibull Distribution”, Communications Series A1 Mathematics & Statistics, 69, 794-814.
  • Asgharzadeh, A., Rezaie, R., Abdi, M., (2011). “Comparisons of methods of estimation for the half-logistic distribution”, Selçuk Journal of Applied Mathematics, 93-108.
  • Bebbington, M., Lai, C. D., Zitikis, R., (2007). “A flexible Weibull extension,” “Reliability Engineering & System Safety”, 92, 719-726.
  • Bjerkedal, T., (1960). “Acquisition of Resistance in Guinea Piesinfected with Different Doses of Virulent Tubercle Bacill”, American Journal of Hygiene, 72, 130-148.
  • Khaleel, M. A., Oguntunde,, P. E., Ahmed,, M.T., Ibrahim, N.A., Loh Y.F., (2020). “The Gompertz Flexible Weibull Distribution and its Applications,” Malaysian Journal of Mathematical Sciences, 14, 169-190.
  • Kundu, D., Raqab, M. Z., (2009). “Estimation of R = P(Y < X) for three parameter Weibull distribution”, Stat. Probab. Lett., 79, 1839–1846.
  • Kurban, M., Kanta, Y., Hocaoğlu, F. O., (2007). “Weibull Dagılımı Kullanılarak Rüzgar Hız ve Güç Yoğunluklarının İstatistiksel Analizi”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 7, 205-218.
  • Lawless, J. F., (1982). “Statistical Models and Methods for Lifetime Data”, Second ed., Wiley, New York.
  • Nassar, M., Afify, A. Z., Dey, S., Kumar, D., (2018). “A new extension of Weibull distribution: properties and different methods of estimation”, Journal of Computational and Applied Mathematics, 336, 439-457.
  • Nichols, M. D., Padgett, W. J., (2006). “A bootstrap control chart for Weibull percentiles”, Quality and Reliability Engineering International, 22, 141-151.
  • Peng X., Yan, Z., (2014). “Estimation and application for a new extended Weibull distribution,” Reliability Engineering & System Safety, 121, 34-42.
  • Taniş, C., Saracoglu, B., (2019). “Comparisons of six different estimation methods for log-Kumaraswamy distribution”, Thermal Science, 23, 1839-1847.
  • Xu, K. Xie, M., Tang, L. C., Ho, S. L., (2003). “Application of neural networks in forecasting engine systems reliability”, Applied Soft Computing, 2, 255-268.
There are 13 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Makaleler
Authors

Caner Tanış 0000-0003-0090-1661

Kadir Karakaya 0000-0002-0781-3587

Publication Date December 18, 2021
Published in Issue Year 2021 Volume: 14 Issue: 3

Cite

APA Tanış, C., & Karakaya, K. (2021). A Comparison of Estimation Methods for Gompertz Flexible Weibull Distribution. Erzincan University Journal of Science and Technology, 14(3), 887-897. https://doi.org/10.18185/erzifbed.777540