DUS Inverse Weibull Distribution and Parameter Estimation in Regression Model

Öz

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.

Anahtar Kelimeler

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

DUS Inverse Weibull Dağılımı ve Lineer Regresyonda Parametre Tahmini

Öz

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.

Anahtar Kelimeler

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

Kaynakça

1. [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. [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. [3] Gul, H. H. 2020. DUS Weibull and DUS Inverse Weibull Distributions: Parameter Estimation and Hypothesis Tests. PhD. Thesis, Gazi University, Ankara, Turkey.
4. [4] Nadarajah, S., Gupta, A. K. 2004. The beta Fréchet distribution. Far east journal of theoretical statistics, 14(1), 15-24.
5. [5] Nadarajah, S., Kotz, S. 2006. The exponentiated type distributions. Acta Applicandae Mathematica, 92(2), 97-111.
6. [6] De Gusmao, F. R., Ortega, E. M., Cordeiro, G. M. 2011. The generalized inverse Weibull distribution. Statistical Papers, 52(3), 591-619.
7. [7] Mahmoud, M. R., Mandouh, R. M. 2013. On the transmuted Fréchet distribution. Journal of Applied Sciences Research, 9(10), 5553-5561.
8. [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. [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. [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. [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. [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. [13] Wolfowitz, J. 1953. Estimation by the minimum distance method. Annals of The Institute of Statistical Mathematics, 5(1), 9-23.
14. [14] Wolfowitz, J. 1957. The minimum distance method. The Annals of Mathematical Statistics, 28, 75-88.
15. [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. [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.