SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2019 / Cilt: 68 - Sayı: 1

Maximum Lq-Likelihood Estimation for the parameters of Marshall-Olkin Extended Burr XII Distribution

Şenay ÖZDEMİR
Yeşim GÜNEY
Yetkin TUAÇ
Olcay ARSLAN
Pages
17–34
Publication Date
2019-02-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

According to our results MLq estimation method is a good alternative to the maximum likelihood and M estimation methods in the presence of outliers.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Marshall--Olkin extended Burr XII (MOEBXII) distribution is proposed by Al-Saiari et al. (2014) to obtain a more flexible family of distributions.
📊
Key Findings & Data:We give some simulation studies and a real data example to compare the performance of the MLq estimators with the maximum likelihood and M estimators.
💡
Conclusion & Impact:According to our results MLq estimation method is a good alternative to the maximum likelihood and M estimation methods in the presence of outliers.
🔬Design:Research Article
📍Scope:2014 Verileri
⚙️Variables:Marshall-Olkin extended Burr XII (MOEBXII) distribution · maximum Lq estimation · maximum likelihood estimator

Abstract

Marshall--Olkin extended Burr XII (MOEBXII) distribution is proposed by Al-Saiari et al. (2014) to obtain a more flexible family of distributions. Some estimation methods like maximum likelihood, Bayes and M estimations are used to estimate the parameters of the MOEBXII distribution in literature. In this paper, we propose to use Maximum Lq (MLq) estimation method to find alternative estimators for the parameters of the MOEBXII distribution. We give some simulation studies and a real data example to compare the performance of the MLq estimators with the maximum likelihood and M estimators. According to our results MLq estimation method is a good alternative to the maximum likelihood and M estimation methods in the presence of outliers.

🔖

Cite This Article

ÖZDEMİR, Ş., GÜNEY, Y., TUAÇ, Y., ARSLAN, O. (2019). Maximum Lq-Likelihood Estimation for the parameters of Marshall-Olkin Extended Burr XII Distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 68 - Sayı: 1, 17–34. https://ajindex.com/articles/747015

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (10)

  1. Al-Hussaini, E. K. and Jaheen, Z. F., Bayes Estimation of the Parameters, Reliability and Failure Rate Functions of the Burr Type XII Failure Model, Journal of Statistical Computation and Simulation (1992), 41 (1-2), 31-40.
  2. Al-Saiari, A. Y., Baharith, L. A. and Mousa, S. A., Marshall-Olkin Extended Burr Type XII Distribution, International Journal of Statistics and Probability (2014), 3 (1), 78-84.
  3. Burr, W., Cumulative Frequency Functions, The Annals of Mathematical Statistics (1942), 1 (2), 215-232.
  4. Caroni, C., Testing for the Marshall--Olkin extended form of the Weibull distribution, Stat. Papers (2010), 51, 325--336. CO₂ emission data for 34 countries access: http://ec.europa.eu/eurostat/tgm/table.do?tab= table&init=1&plugin=1&language=en&pcode=tsdcc100 Dogru, F. Z. and Arslan, O., Alternative Robust Estimators for the Shape Parameters of the Burr XII Distribution, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering (2015), 9 (5), 271-276.
  5. Ferrari, D. and Yang, Y., Maximum lq-likelihood estimation, The Annals of Statistics (2010), 38, 753--783. Ferrari, D. and Paterlini, S., The maximum lq-likelihood method: an application to extreme quantile estimation in finance, Methodology and Computing in Applied Probability (2009), 11(1), 3--19. Ghitany, M. E., Marshall Olkin Extended Pareto and Its Application, International Journal of Applied Mathematics (2005), 18(1), 17-32.
  6. Ghitany, M. E., Al-Hussaini E. K., and AlJarallah.R. A., Marshall--Olkin extended Weibull distribution and its application to censored data, J. Appl. Stat. (2005), 1025--1034. Ghitany, M. E., Al-Awadhi, F. A. and Alkhalfan L. A., Marshall--olkin extended lomax distribution and its application to censored data, Communications in Statistics Theory and Methods (2007), 36(10), 1855-1866.
  7. Gui, W., Marshall-Olkin Extended Log-Logistic Distribution and Its Application in Minification Processes, Applied Mathematical Sciences (2013), 7(80), 3947-3961.
  8. Gupta, P. L., Gupta, R. C. and Lvin, S. J., Analysis of failure time data by burr distribution, Communications in Statistics-Theory and Methods (1996), 25, 2013-2024.
  9. Gupta, R. C., Ghitany, M. E., and Al-Mutairi D. K., Estimation of reliability from Marshall-Olkin extended Lomax distribution, Journal of Statistical Computation and Simulation (2010), 80(8), 937-947.
  10. Güney, Y. and Arslan, O., Robust parameter estimation for the Marshall-Olkin extended Burr XII distribution,Commun.Fac.Sci.Univ.Ank.Series A1