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This paper discussed robust estimation for point estimation of the shape and scale parameters for generalized exponential (GE) distribution using a complete dataset in the presence of various percentages of outliers. In the case of outliers, it is known that classical methods such as maximum likelihood estimation (MLE), least square (LS) and maximum product spacing (MPS) in case of outliers cannot reach the best estimator. To confirm this fact, these classical methods were applied to the data of this study and compared with non-classical estimation methods. The non-classical (Robust) methods such as least absolute deviations (LAD), and M-estimation (using M. Huber (MH) weight and M. Bisquare (MB) weight) had been introduced to obtain the best estimation method for the parameters of the GE distribution. The comparison was done numerically by using the Monte Carlo simulation study. The two real datasets application confirmed that the M-estimation method is very much suitable for estimating the GE parameters. We concluded that the M-estimation method using Huber object function is a suitable estimation method in estimating the parameters of the GE distribution for a complete dataset in the presence of various percentages of outliers.
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- Ahmad, N. (2010). Designing accelerated life tests for generalised exponential distribution with log-linear model. International Journal of Reliability and Safety, 4(2-3), 238-264.
- Aydın, D., Akgül, F. G., & Şenoğlu, B. (2018). Robust estimation of the location and the scale parameters of shifted Gompertz distribution. Electronic Journal of Applied Statistical Analysis, 11(1), 92-107.
- Ahmad, H. H., & Almetwally, E. (2020). Marshall-Olkin Generalized Pareto Distribution: Bayesian and Non Bayesian Estimation. Pakistan Journal of Statistics and Operation Research, 21-33.
- Almetwally, E. M., & Almogy, H. M. (2018). Comparison between M-estimation, S-estimation, And MM Estimation Methods of Robust Estimation with Application and Simulation. International Journal of Mathematical Archive, 9(11), 55-63.
- Almetwally, E. M., & Almongy, H. M. (2019). Estimation method for new Weibull-Pareto distribution: Simulation and application. Journal of Data Scince. 17(3), 610-630.
- Almetwally, E. M., Almongy, H. M., & El sayed Mubarak, A. (2018). Bayesian and maximum likelihood estimation for the Weibull generalized exponential distribution parameters using progressive censoring schemes. Pakistan Journal of Statistics and Operation Research, 15(4) 853-868.
- Basheer, A. M., Almetwally, E. M., & Okasha, H. M. (2020) Marshall-Olkin Alpha Power Inverse Weibull Distribution: Non Bayesian and Bayesian Estimations. journal of Statistics Applications & Probability, To appear.
- Chen, D. G., & Lio, Y. L. (2010). Parameter estimations for generalized exponential distribution under progressive type-I interval censoring. Computational Statistics & Data Analysis, 54(6), 1581-1591.
- Cheng, R. C. H., & Amin, N. A. K. (1983). Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society: Series B (Methodological), 45(3), 394-403.
- Dodge, Y. (2008). The concise encyclopedia of statistics. Springer Science & Business Media.
- El-Sherpieny, E. S. A., Almetwally, E. M., & Muhammed, H. Z. (2020). Progressive Type-II hybrid censored schemes based on maximum product spacing with application to Power Lomax distribution. Physica A: Statistical Mechanics and its Applications, 553(1), 124251.
- Fang, Y., & Zhao, L. (2006). Approximation to the distribution of LAD estimators for censored regression by random weighting method. Journal of statistical planning and inference, 136(4), 1302-1316.
- Gupta, R. C., Kannan, N., & Raychaudhuri, A. (1997). Analysis of lognormal survival data. Mathematical biosciences, 139(2), 103-115.
- Gupta, R. D., & Kundu, D. (1999). Theory & methods: Generalized exponential distributions. Australian & New Zealand Journal of Statistics, 41(2), 173-188.
- Gupta, R. D., & Kundu, D. (2001). Generalized exponential distribution: different method of estimations. Journal of Statistical Computation and Simulation, 69(4), 315-337.
- Hossain, S. A. (2018). Estimating the Parameters of a Generalized Exponential Distribution. Journal of Statistical Theory and Applications, 17(3), 537-553.
- Huber, P. J. (1964). Robust estimation of a location parameter. Mathemat. Statist. 35:73–101.
- Huber, P.J. (1981). Robust Statistics, Wiley, New York.
- Jorgensen, B. (2012). Statistical properties of the generalized inverse Gaussian distribution (Vol. 9). Springer Science & Business Media.
- Kantar, Y. M., & Yildirim, V. (2015). Robust Estimation for Parameters of the Extended Burr Type III Distribution. Communications in Statistics-Simulation and Computation, 44(7), 1901-1930.
- Kundu, D., & Gupta, R. D. (2008). Generalized exponential distribution: Bayesian estimations. Computational Statistics & Data Analysis, 52(4), 1873-1883.
- Kundu, D., & Gupta, R. D. (2011). An extension of the generalized exponential distribution. Statistical Methodology, 8(6), 485-496.
- Kundu, D., & Nekoukhou, V. (2018). Univariate and bivariate geometric discrete generalized exponential distributions. Journal of Statistical Theory and Practice, 12(3), 595-614.
- Naqash, S., Ahmad, S. P., & Ahmed, A. (2016). Bayesian Analysis of Generalized Exponential Distribution. Journal of Modern Applied Statistical Methods, 15(2), 38.
- Tahir, M. H., Cordeiro, G. M., Alizadeh, M., Mansoor, M., Zubair, M., & Hamedani, G. G. (2015). The odd generalized exponential family of distributions with applications. Journal of Statistical Distributions and Applications, 2(1), 1.
- Valiollahi, R., Asgharzadeh, A., & Kundu, D. (2017). Prediction of future failures for generalized exponential distribution under Type-I or Type-II hybrid censoring. Brazilian Journal of Probability and Statistics, 31(1), 41-61.
- Wang, F. K., & Lee, C. W. (2010). An M-estimation for Estimating the Extended Burr Type III Parameters with Outliers. Communications in Statistics-Theory and Methods, 40(2), 304-322.
- Wang, F. K., & Lee, C. W. (2011). M-estimation with asymmetric influence function for estimating the Burr type III parameters with outliers. Computers & Mathematics with Applications, 62(4), 1896-1907.
- Wang, F. K., & Lee, C. W. (2014). M-estimation for estimating the Burr type III parameters with outliers. Mathematics and Computers in Simulation, 105, 144-159.