ROBUST PARAMETER ESTIMATION FOR THE MARSHALL-OLKIN EXTENDED BURR XII DISTRIBUTION

Year 2017, Volume: 66 Issue: 2, 141 - 161, 01.08.2017

Yeşim Güney Olcay Arslan

https://doi.org/10.1501/Commua1_0000000808

Cited By: 1

Abstract

In this paper, we consider the parameter estimation of the Marshall–Olkin extended Burr XII (MOEBXII) distribution, which is a generalizationof the Burr XII distribution.For the estimation of the parameters in theMOEBXII, maximum likelihood (ML) is available. However, this is not robustestimator. In this paper we proposed a robust estimator based on M estimation method to estimate the parameters of the MOEBXII distribution. Weperform a small simulation study to illustrate the performance of proposedmethod. We also reanalyze two data sets to asses the capability of the robustestimators over the ML and LS estimators

Keywords

Marshall-Olkin extended Burr XII (MOEBXII) distribution, robustestimator, maximum likelihood estimator, least squares estimator

References

• 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 Computa- tion and Simulation (1992), 41 (1-2), 31-40.
• 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.
• Burr, W., Cumulative Frequency Functions, The Annals of Mathematical Statistics (1942), 1 (2), 215-232.
• 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.
• Dogru, F. Z. and Arslan, O., Optimal B-robust estimators for the parameters of the Burr XII distribution. Journal of Statistical Computation and Simulation (2016), 86 (6), 1133-1149.
• Ghitany, M.E., Al-Awadhi, F.A. and Alkhalfan L.A., Marshall–olkin extended lomax distrib- ution and its application to censored data, Communications in Statistics Theory and Methods (2007), 36 (10), 1855-1866.
• Gui, W., Marshall-Olkin Extended Log-Logistic Distribution and Its Application in Mini…- cation Processes. Applied Mathematical Sciences (2013), 7 (80), 3947-3961.
• 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
• Hossain, A. M. and Nath, S. K., Estimation of parameters in the presence of outliers for a burr XII distribution, Communications in Statistics - Theory and Methods (1997), 26 (3), 637-652.
• Huber, P. J., Robust estimation of a location parameter, Ann. Math. Statist. (1964), 35, 73-101.
• Klugman, S. A., Loss Distributions. Proceedings of Symposia in Applied Mathematics Actu- arial Mathematics (1986), 35, 31-55.
• Lawless, J. F., Statistical Models and Methods for Lifetime Data. New York: John Wiley, 2003.
• Malinowska, I., Pawlas, P. and Szynal D., Estimation of location and scale parameters for the Burr XII distribution using generalized order statistics, Linear Algebra and its Applications (2006), 417 (1), 150-162.
• Marshall, A.W. and Olkin, I., A new method for adding a parameter to a family of distrib- utions with application to the exponential and weibull families, Biometrika (1997), 84 (3), 641-652.
• McDonald, J. B., Some Generalized Function for the Size Distribution of Income, Economet- rica (1984), 52 (3), 647-663.
• Moore, D. and Papadopoulos, A. S., The Burr Type XII Distribution as a Failure Model under Various Loss Functions, Microelectronics Reliability (2000), 40 (12), 2117-2122.
• Papadopoulos, A. S., The Burr Distribution as a Life Time Model from a Bayesian Approach, IEEE Transactions on Reliability (1978), 27 (5), 369-371.
• Rodriguez, R. N., A guide to Burr XII distribution, Biometrika (1977), 64, 129-134.
• Shah, A. and Gokhale, D. V., On maximum product of spagings (mps) estimation for burr xii distributions, Communications in Statistics- Simulation and Computation (1993), 22 (3), 615-641.
• Silva, R. B. and Cordeiro, G. M., The Burr XII power series distributions: A new compound- ing family, Brazilian Journal of Probability and Statistics (2015), 29 (3), 565-589.
• Tadikamalla P. R., A Look at the Burr and Related Distributions, Int. Stat. Rev. (1980), 48(3), 337-344.
• Wingo, D. R., Maximum likelihood methods for …tting the Burr type XII distribution to life test data, Biometrical Journal (1983), 25 (1), 77–84.
• Wingo, D. R., Maximum likelihood methods for …tting the Burr type XII distribution to multiply (progressively) censored life test data, Metrika (1993), 40, 203–210.
• Current address : Ye¸sim Güney (Corresponding author): Ankara University, Faculty of Sci- ences, Department of Statistics 06100 Besevler ANKARA TURKEY.
• E-mail address : [e-mail]
• Current address : Olcay Arslan: Ankara University, Faculty of Sciences, Department of Statis- tics 06100 Besevler ANKARA TURKEY.
• E-mail address : [e-mail]