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Alternative estimation methods for the estimation of Frechet distribution parameters

Yıl 2018, Cilt: 11 Sayı: 2, 109 - 120, 31.12.2018

Öz

In this study, the shape parameter of the Frechet distribution is estimated using simple linear regression model. The ordinary least squares (OLS) and robust estimation method M estimator are considered as the estimation method. Simulation study is conducted to compare effectiveness of estimator based on data set with and without outliers. As a result, it is seen from the simulation result that robust estimation method is more effective than the OLS.

Kaynakça

  • [1] T. Kernane, Z. Raizah, 2014, Estimation of the Parameters of Extreme Value Distributions from Truncated Data Via the EM Algorithm Estimation of the Parameters of Extreme Value Distributions from Truncated Data Via the EM Algorithm, [https://hal.archives-ouvertes.fr/hal-00503252v2/document].
  • [2] M. Frechet, 1927, Sur la loi de probabilite de lecart maximum, Ann. Soc. Polon. Math, 6(93) [https://www.statisticshowto.datasciencecentral.com/frechet-distribution/]
  • [3] K. Abbas, T. Yincai, 2012, Comparison of Estimation Methods for Frechet Distribution with Known Shape, Caspian Journal of Applied Sciences Research, 1(10), pp. 58-64.
  • [4] S. Kotz, S. Nadarajah, 2000, Extreme Value Distributions Theory and Applications, Imperial College Press, Singapure.
  • [5] D.G. Harlow, 2002, Applications of the Frechet distribution function, Int. J. of Materials & Product Technology, 17, 482-495.
  • [6] A. Zaharim, S.K. Najid, A.M. Razali, K. Sopian, 2009, Analyzing malaysian wind speed data using statistical distribution, In Proceedings of the 4th IASME/WSEAS International conference on Energy and Environment. University of Cambridge, February, 24-26
  • [7] S. Nadarajah, S. Kotz, 2008, Sociological models based on Fréchet random variables, Qual Quant, 42, 89–95.
  • [8] F.G. Akgül, B. Şenoğlu (2018) Comparison of Estimation Methods for Inverse Weibull Distribution. In: Tez M., von Rosen D. (eds) Trends and Perspectives in Linear Statistical Inference. Contributions to Statistics. Springer, Cham.
  • [9] M. Mubarak, 2011, Estimation of the Frechet distribution parameters based on record values, Arabian Journal for Science and Engineering, 36,1597–1606.
  • [10] C. Chatterjee , A. Chatterjee, 2012, Use of the Frechet distribution for UPV measurements in concrete. NDT&E International, 52, 122-128.
  • [11] R.B. Silva, M. Bourguignon, G.M. Cordeiro, 2014, Fréchet and ınverse gamma distributions: correct selection and minimum sample size to discriminate them, Journal of Statistical Theory and Practice, 9(1), 73-87.
  • [12] K. Abbas, Y. Tang, 2015, Analysis of Frechet Distribution Using Reference Priors, Communications in Statistics - Theory and Methods, 44(14), 2945-2956.
  • [13] A. Z. Afify, H. M. Yousof, G. M. Cordeiro, E. M. M. Ortega, Z. M. Nofal, 2016, The Weibull Fréchet distribution and its applications, Journal of Applied Statistics, Volume 43, 2608-2626.
  • [14] S. Pindado, C. Pindado, J. Cubas, 2017, Fréchet distribution applied to salary ıncomes in spain from 1999 to 2014. an engineering approach to changes in salaries’ distribution, Economies, 5(14),1-19.
  • [15] F. Maleki, E. Deiri, 2017, Efficient Estimation of the pdf and the cdf of the Frechet Distribution, Annals of Data Science, 4(2),211–225.
  • [16] M. Zayed, N.S Butt, 2017, The Extended Frechet Distribution: Properties and Applications, Pakistan Journal of Statistics and Operation Research, 3, 529-543.
  • [17] M.A. Haq, H.M. Yousof, S. Hashmi, 2017, A New Five-Parameter Fréchet Model for Extreme Values, Pakistan Journal of Statistics and Operation Research 13(3), 617-632.
  • [18] C. J. Tablada, G.M. Cordeiro, 2017, The modified Fréchet distribution and its properties, Communications in Statistics- Theory and Methods, 46, 21,
  • [19] P.L. Ramos, F. Louzadaa, E. Ramosa and S. Dey, 2018, The Frechet distribution: Estimation and Application an Overview, arXiv:1801.05327 [stat.AP].
  • [20] C. Lawson, J.B. Keats, D.C. Montgomery, 1997, Comparison of Robust and Least Squares Regression in Computer-Generated Probability Plots, IEEE Transactions on Reliability, 46 (1), 108-121.
  • [21] A. A. Yavuz (2013), Estimation of the Shape Parameter of the Weibull Distribution Using Linear Regression Methods: Non‐Censored Samples. Qual. Reliab. Engng. Int., 29: 1207-1219. doi:10.1002/qre.1472.
  • [22] A. Benard, E.C. Bos-Levenbach, 1953, The plotting of observations on probability paper. Statistica Neerlandica 7,163–173.
  • [23] P.J. Huber, E.M. Ronchetti, 2009, Robust Statistics, Wiley Series in Probability and Statistics. 2nd Edition, John Wiley & Sons, Inc., Hoboken.
  • [24] D.N. Gujerati, D.C. Porter, 2016, Temel ekonometri, 5. Basım, Literatür yayıncılık, İstanbul

Frechet dağılımının şekil parametresinin tahmini için alternatif tahmin yöntemi

Yıl 2018, Cilt: 11 Sayı: 2, 109 - 120, 31.12.2018

Öz

Bu çalışmada Frechet dağılımının şekil parametresi basit doğrusal regresyon modeli kullanılarak tahmin edilmiştir. Tahmin yöntemi olarak En Küçük Kareler (EKK) ve sağlam (robust) tahmin yöntemi olan M tahmin edicisi ele alınmıştır. Bu tahmin yöntemlerinin etkinlikleri veri setinin aykırı değer içerip içermeme durumuna göre simülasyon çalışması ile karşılaştırılmıştır. Sonuç olarak Frechet dağılımının şekil parametresinin tahmininde yapılan simülasyon çalışması ile sağlam yöntemin parametre tahminin EKK’dan daha etkin olduğu görülmüştür.

Kaynakça

  • [1] T. Kernane, Z. Raizah, 2014, Estimation of the Parameters of Extreme Value Distributions from Truncated Data Via the EM Algorithm Estimation of the Parameters of Extreme Value Distributions from Truncated Data Via the EM Algorithm, [https://hal.archives-ouvertes.fr/hal-00503252v2/document].
  • [2] M. Frechet, 1927, Sur la loi de probabilite de lecart maximum, Ann. Soc. Polon. Math, 6(93) [https://www.statisticshowto.datasciencecentral.com/frechet-distribution/]
  • [3] K. Abbas, T. Yincai, 2012, Comparison of Estimation Methods for Frechet Distribution with Known Shape, Caspian Journal of Applied Sciences Research, 1(10), pp. 58-64.
  • [4] S. Kotz, S. Nadarajah, 2000, Extreme Value Distributions Theory and Applications, Imperial College Press, Singapure.
  • [5] D.G. Harlow, 2002, Applications of the Frechet distribution function, Int. J. of Materials & Product Technology, 17, 482-495.
  • [6] A. Zaharim, S.K. Najid, A.M. Razali, K. Sopian, 2009, Analyzing malaysian wind speed data using statistical distribution, In Proceedings of the 4th IASME/WSEAS International conference on Energy and Environment. University of Cambridge, February, 24-26
  • [7] S. Nadarajah, S. Kotz, 2008, Sociological models based on Fréchet random variables, Qual Quant, 42, 89–95.
  • [8] F.G. Akgül, B. Şenoğlu (2018) Comparison of Estimation Methods for Inverse Weibull Distribution. In: Tez M., von Rosen D. (eds) Trends and Perspectives in Linear Statistical Inference. Contributions to Statistics. Springer, Cham.
  • [9] M. Mubarak, 2011, Estimation of the Frechet distribution parameters based on record values, Arabian Journal for Science and Engineering, 36,1597–1606.
  • [10] C. Chatterjee , A. Chatterjee, 2012, Use of the Frechet distribution for UPV measurements in concrete. NDT&E International, 52, 122-128.
  • [11] R.B. Silva, M. Bourguignon, G.M. Cordeiro, 2014, Fréchet and ınverse gamma distributions: correct selection and minimum sample size to discriminate them, Journal of Statistical Theory and Practice, 9(1), 73-87.
  • [12] K. Abbas, Y. Tang, 2015, Analysis of Frechet Distribution Using Reference Priors, Communications in Statistics - Theory and Methods, 44(14), 2945-2956.
  • [13] A. Z. Afify, H. M. Yousof, G. M. Cordeiro, E. M. M. Ortega, Z. M. Nofal, 2016, The Weibull Fréchet distribution and its applications, Journal of Applied Statistics, Volume 43, 2608-2626.
  • [14] S. Pindado, C. Pindado, J. Cubas, 2017, Fréchet distribution applied to salary ıncomes in spain from 1999 to 2014. an engineering approach to changes in salaries’ distribution, Economies, 5(14),1-19.
  • [15] F. Maleki, E. Deiri, 2017, Efficient Estimation of the pdf and the cdf of the Frechet Distribution, Annals of Data Science, 4(2),211–225.
  • [16] M. Zayed, N.S Butt, 2017, The Extended Frechet Distribution: Properties and Applications, Pakistan Journal of Statistics and Operation Research, 3, 529-543.
  • [17] M.A. Haq, H.M. Yousof, S. Hashmi, 2017, A New Five-Parameter Fréchet Model for Extreme Values, Pakistan Journal of Statistics and Operation Research 13(3), 617-632.
  • [18] C. J. Tablada, G.M. Cordeiro, 2017, The modified Fréchet distribution and its properties, Communications in Statistics- Theory and Methods, 46, 21,
  • [19] P.L. Ramos, F. Louzadaa, E. Ramosa and S. Dey, 2018, The Frechet distribution: Estimation and Application an Overview, arXiv:1801.05327 [stat.AP].
  • [20] C. Lawson, J.B. Keats, D.C. Montgomery, 1997, Comparison of Robust and Least Squares Regression in Computer-Generated Probability Plots, IEEE Transactions on Reliability, 46 (1), 108-121.
  • [21] A. A. Yavuz (2013), Estimation of the Shape Parameter of the Weibull Distribution Using Linear Regression Methods: Non‐Censored Samples. Qual. Reliab. Engng. Int., 29: 1207-1219. doi:10.1002/qre.1472.
  • [22] A. Benard, E.C. Bos-Levenbach, 1953, The plotting of observations on probability paper. Statistica Neerlandica 7,163–173.
  • [23] P.J. Huber, E.M. Ronchetti, 2009, Robust Statistics, Wiley Series in Probability and Statistics. 2nd Edition, John Wiley & Sons, Inc., Hoboken.
  • [24] D.N. Gujerati, D.C. Porter, 2016, Temel ekonometri, 5. Basım, Literatür yayıncılık, İstanbul
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Arzu Altın Yavuz 0000-0002-3277-740X

Ebru Gündoğan Aşık 0000-0002-0545-7339

Y. Murat Bulut 0000-0002-9910-6555

Yayımlanma Tarihi 31 Aralık 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 11 Sayı: 2

Kaynak Göster

IEEE A. A. Yavuz, E. G. Aşık, ve Y. M. Bulut, “Frechet dağılımının şekil parametresinin tahmini için alternatif tahmin yöntemi”, JSSA, c. 11, sy. 2, ss. 109–120, 2018.