Abstract
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.
Highlights
Gupta and Kundu (1999) introduced a two-parameter Generalized Exponential (GE) distribution, which is one of the most popular distributions and it has been used quite effectively for analyzing lifetime datasets
We present various parameter estimation methods for the generalized exponential distribution using a complete dataset in the presence of outliers
The Monte Carlo simulation results showed that the M-estimation method using the Huber objective function outperformed the other methods in terms of Bias and MSE values
Summary
Gupta and Kundu (1999) introduced a two-parameter Generalized Exponential (GE) distribution, which is one of the most popular distributions and it has been used quite effectively for analyzing lifetime datasets. Gupta and Kundu (2001) discussed different methods of estimation such as MLE, LS, Moment, Weighted Least Squares methods for the parameters of a GE distribution. The common estimation methods would not be appropriate in solving the parameter estimation problem if data have contained outliers or extreme observations. The final motivation of the paper is to develop a guideline for introducing the best estimation method for GE distribution, where the data contains outliers or extreme observations. The paper is organized as follows: section 2 is devoted to the GE parameters estimation using the MLE method, the LS method and the MPS method, while in section 3 the robust estimation is considered. The Classical Estimation Methods the parameter estimation by MLE, LS and MPS estimation methods will be discussed
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