Using Wavelet Shrinkage to Deal with Contamination Problem in Survival Function for Weibull Distribution
Abstract
In this paper, the survival function of the Weibull distribution was estimated by the Classical Maximum Likelihood Estimate Method for the scale and shape parameters, and then the efficiency of the estimated parameters was calculated based on the mean square error and compared with the proposed method that deals with the contamination problem before estimating the parameters of the survival function for Weibull distribution through the use of Wavelets (Daubechies2), (Symlet3), and (Coiflit4) with several different methods of estimating the level of thresholding depending on the rule of soft. For the purpose of estimating and comparing the efficiency of the proposed method with the classical method, simulations were carried out for several different cases of the values for scale and shape parameters of Weibull distribution, contamination percentages, and different sample sizes as well as real data based on a MATLAB code designed for this purpose, the statistical program (SPSS) and the (Easy Fit) program. The study showed the efficiency of the precision parameters estimate for Weibull distribution when there was a data contamination problem when using the proposed method compared to the classical method..
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