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DUS Inverse Weibull Distribution and Parameter Estimation in Regression Model

Year 2023, Volume: 27 Issue: 1, 42 - 50, 25.04.2023

Hasan Hüseyin Gül Şükrü Acıtaş Hülya Bayrak Birdal Şenoğlu

https://doi.org/10.19113/sdufenbed.1107862

Abstract

This paper considers various estimation methods to estimate the unknown parameters of the DUS Inverse Weibull (DIW) distribution using the maximum likelihood (ML), least squares (LS), weighted least squares (WLS), Cramer-von Mises (CVM) and the Anderson-Darling (AD) estimators. A Monte-Carlo simulation study is conducted to determine the most preferable estimators in terms of their efficiencies. Furthermore, the distribution of the error terms in the simple linear regression is assumed to be DIW to show the implementation of it to the linear models. We also carry out a simulation study for comparing the performances of the estimators of the unknown regression parameters.

Keywords

DUS transformation Inverse Weibull Parameter estimation Lineer regression Monte-Carlo simulation

References

  • [1] Kumar, D., Singh, U., Singh, S. K. 2015. A method of proposing new distribution and its application to Bladder cancer patient’s data. Journal of Statistics Applications & Probability Letters, 2(3), 235-245.
  • [2] Gul, H. H., Acitas, S., Senoglu, B., Bayrak, H. 2018. DUS Inverse Weibull distribution and its applications. 19th International Symposium on Econometrics, Operation Research and Statistics, Antalya, Turkey, 743-745.
  • [3] Gul, H. H. 2020. DUS Weibull and DUS Inverse Weibull Distributions: Parameter Estimation and Hypothesis Tests. PhD. Thesis, Gazi University, Ankara, Turkey.
  • [4] Nadarajah, S., Gupta, A. K. 2004. The beta Fréchet distribution. Far east journal of theoretical statistics, 14(1), 15-24.
  • [5] Nadarajah, S., Kotz, S. 2006. The exponentiated type distributions. Acta Applicandae Mathematica, 92(2), 97-111.
  • [6] De Gusmao, F. R., Ortega, E. M., Cordeiro, G. M. 2011. The generalized inverse Weibull distribution. Statistical Papers, 52(3), 591-619.
  • [7] Mahmoud, M. R., Mandouh, R. M. 2013. On the transmuted Fréchet distribution. Journal of Applied Sciences Research, 9(10), 5553-5561.
  • [8] Krishna, E., Jose, K. K., Alice, T., Ristić, M. M. 2013. The Marshall-Olkin Fréchet distribution. Communications in Statistics-Theory and Methods, 42(22), 4091-4107.
  • [9] Tiku, M. L., Islam, M. Q., Selçuk, A. S. 2001. Nonnormal regression. II. Symmetric distributions. Communications in Statistics-Theory and Methods, 30(6), 1021-1045,
  • [10] Islam, M. Q., Tiku, M. L., Yildirim, F. 2001. Nonnormal regression. I. Skew distributions. Communications in Statistics-Theory and Methods, 30(6), 993-1020
  • [11] Gul, H. H., Acitas, S., Senoglu, B., Bayrak, H. 2019. Parameter estimation in simple linear regression model under nonnormal error terms. Çukurova II. Multidisciplinary Studies Congress, Adana, Turkey, 268-270.
  • [12] Swain, J. J., Venkatraman, S., Wilson, J. R. 1988. Least-squares estimation of distribution functions in Johnson's translation system. Journal of Statistical Computation and Simulation, 29(4), 271-297.
  • [13] Wolfowitz, J. 1953. Estimation by the minimum distance method. Annals of The Institute of Statistical Mathematics, 5(1), 9-23.
  • [14] Wolfowitz, J. 1957. The minimum distance method. The Annals of Mathematical Statistics, 28, 75-88.
  • [15] Luceno, A. 2006. Fitting the generalized Pareto distribution to data using maximum goodness-of-fit estimators. Computational Statistics & Data Analysis, 51(2), 904-917.
  • [16] Kantar, Y. M., Senoglu B. 2008. A comparative study for the location and scale parameters of the Weibull distribution with given shape parameter. Computer & Geosciences, 34, 1900-1909.

DUS Inverse Weibull Dağılımı ve Lineer Regresyonda Parametre Tahmini

Year 2023, Volume: 27 Issue: 1, 42 - 50, 25.04.2023

Hasan Hüseyin Gül Şükrü Acıtaş Hülya Bayrak Birdal Şenoğlu

https://doi.org/10.19113/sdufenbed.1107862

Abstract

Bu çalışma, en çok olabilirlik (ML), en küçük kareler (LS), ağırlıklı en küçük kareler (WLS), Cramer-von Mises (CM) ve Anderson-Darling (AD) tahmin edicilerini kullanarak DUS Inverse Weibull (DIW) dağılımının bilinmeyen parametrelerini tahmin etmek için çeşitli tahmin yöntemlerini ele almaktadır. Etkinlikleri açısından en çok tercih edilen tahmin edicileri belirlemek için bir Monte-Carlo simülasyon çalışması yapılmıştır. Ayrıca, lineer modellere uygulanışını göstermek için basit lineer regresyonda hata terimlerinin dağılımının DIW olduğu varsayılmıştır. Bilinmeyen regresyon parametrelerinin tahmin edicilerinin performanslarının karşılaştırılması için de bir simülasyon çalışması yapılmıştır.

Keywords

DUS dönüşümü Inverse Weibull Parametre tahmini Lineer regresyon Monte-Carlo simülasyonu

References

  • [1] Kumar, D., Singh, U., Singh, S. K. 2015. A method of proposing new distribution and its application to Bladder cancer patient’s data. Journal of Statistics Applications & Probability Letters, 2(3), 235-245.
  • [2] Gul, H. H., Acitas, S., Senoglu, B., Bayrak, H. 2018. DUS Inverse Weibull distribution and its applications. 19th International Symposium on Econometrics, Operation Research and Statistics, Antalya, Turkey, 743-745.
  • [3] Gul, H. H. 2020. DUS Weibull and DUS Inverse Weibull Distributions: Parameter Estimation and Hypothesis Tests. PhD. Thesis, Gazi University, Ankara, Turkey.
  • [4] Nadarajah, S., Gupta, A. K. 2004. The beta Fréchet distribution. Far east journal of theoretical statistics, 14(1), 15-24.
  • [5] Nadarajah, S., Kotz, S. 2006. The exponentiated type distributions. Acta Applicandae Mathematica, 92(2), 97-111.
  • [6] De Gusmao, F. R., Ortega, E. M., Cordeiro, G. M. 2011. The generalized inverse Weibull distribution. Statistical Papers, 52(3), 591-619.
  • [7] Mahmoud, M. R., Mandouh, R. M. 2013. On the transmuted Fréchet distribution. Journal of Applied Sciences Research, 9(10), 5553-5561.
  • [8] Krishna, E., Jose, K. K., Alice, T., Ristić, M. M. 2013. The Marshall-Olkin Fréchet distribution. Communications in Statistics-Theory and Methods, 42(22), 4091-4107.
  • [9] Tiku, M. L., Islam, M. Q., Selçuk, A. S. 2001. Nonnormal regression. II. Symmetric distributions. Communications in Statistics-Theory and Methods, 30(6), 1021-1045,
  • [10] Islam, M. Q., Tiku, M. L., Yildirim, F. 2001. Nonnormal regression. I. Skew distributions. Communications in Statistics-Theory and Methods, 30(6), 993-1020
  • [11] Gul, H. H., Acitas, S., Senoglu, B., Bayrak, H. 2019. Parameter estimation in simple linear regression model under nonnormal error terms. Çukurova II. Multidisciplinary Studies Congress, Adana, Turkey, 268-270.
  • [12] Swain, J. J., Venkatraman, S., Wilson, J. R. 1988. Least-squares estimation of distribution functions in Johnson's translation system. Journal of Statistical Computation and Simulation, 29(4), 271-297.
  • [13] Wolfowitz, J. 1953. Estimation by the minimum distance method. Annals of The Institute of Statistical Mathematics, 5(1), 9-23.
  • [14] Wolfowitz, J. 1957. The minimum distance method. The Annals of Mathematical Statistics, 28, 75-88.
  • [15] Luceno, A. 2006. Fitting the generalized Pareto distribution to data using maximum goodness-of-fit estimators. Computational Statistics & Data Analysis, 51(2), 904-917.
  • [16] Kantar, Y. M., Senoglu B. 2008. A comparative study for the location and scale parameters of the Weibull distribution with given shape parameter. Computer & Geosciences, 34, 1900-1909.
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Makaleler
Authors

Hasan Hüseyin Gül 0000-0001-9905-8605

Şükrü Acıtaş 0000-0002-4131-0086

Hülya Bayrak 0000-0001-5666-4250

Birdal Şenoğlu 0000-0003-3707-2393

Publication Date April 25, 2023
Published in Issue Year 2023 Volume: 27 Issue: 1

Cite

APA Gül, H. H., Acıtaş, Ş., Bayrak, H., Şenoğlu, B. (2023). DUS Inverse Weibull Distribution and Parameter Estimation in Regression Model. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 27(1), 42-50. https://doi.org/10.19113/sdufenbed.1107862
AMA Gül HH, Acıtaş Ş, Bayrak H, Şenoğlu B. DUS Inverse Weibull Distribution and Parameter Estimation in Regression Model. SDÜ Fen Bil Enst Der. April 2023;27(1):42-50. doi:10.19113/sdufenbed.1107862
Chicago Gül, Hasan Hüseyin, Şükrü Acıtaş, Hülya Bayrak, and Birdal Şenoğlu. “DUS Inverse Weibull Distribution and Parameter Estimation in Regression Model”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 27, no. 1 (April 2023): 42-50. https://doi.org/10.19113/sdufenbed.1107862.
EndNote Gül HH, Acıtaş Ş, Bayrak H, Şenoğlu B (April 1, 2023) DUS Inverse Weibull Distribution and Parameter Estimation in Regression Model. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 27 1 42–50.
IEEE H. H. Gül, Ş. Acıtaş, H. Bayrak, and B. Şenoğlu, “DUS Inverse Weibull Distribution and Parameter Estimation in Regression Model”, SDÜ Fen Bil Enst Der, vol. 27, no. 1, pp. 42–50, 2023, doi: 10.19113/sdufenbed.1107862.
ISNAD Gül, Hasan Hüseyin et al. “DUS Inverse Weibull Distribution and Parameter Estimation in Regression Model”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 27/1 (April 2023), 42-50. https://doi.org/10.19113/sdufenbed.1107862.
JAMA Gül HH, Acıtaş Ş, Bayrak H, Şenoğlu B. DUS Inverse Weibull Distribution and Parameter Estimation in Regression Model. SDÜ Fen Bil Enst Der. 2023;27:42–50.
MLA Gül, Hasan Hüseyin et al. “DUS Inverse Weibull Distribution and Parameter Estimation in Regression Model”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 27, no. 1, 2023, pp. 42-50, doi:10.19113/sdufenbed.1107862.
Vancouver Gül HH, Acıtaş Ş, Bayrak H, Şenoğlu B. DUS Inverse Weibull Distribution and Parameter Estimation in Regression Model. SDÜ Fen Bil Enst Der. 2023;27(1):42-50.
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