Weighted Likelihood Estimator for Exponentiated Weibull Distribution
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Abstract
Abstract
In this study, we apply the weighted likelihood estimator (WLE) to the Exponentiated Weibull EW distribution with contamination. And we also compare the performance to the maximum likelihood estimator (MLE). We fix the central distribution to be the EW distribution with(2,1,1) and (2,2,2) and the contamination is EW distribution with parameter
where
= 1, 5 and the contamination proportion (
)= 0.01, 0.03, and 0.05 and the values of pre–assigned small probability k= 0.01, 0.03, 0.05 with shape parameter
= 2. We perform a Monte Carlo simulation to compare the perform of MLE and WLE. The simulation results are based on the 10,000 replace. The efficiency of the MLE and WLE are compared based on the bias values and the root mean square error (RMSE). The result show that the sample size increase as the bias and RMSE of the MLE and WLE decrease in all most of the cases. The WLE method for
provide better than MLE result in the term of the bias and RMSE when k is large for the estimator scale parameter (
). While the MLE method for
provide better WLE result in the term of the bias and RMSE for the estimator shape parameter (
).
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