Statistical inference for the size-biased Weibull distribution |
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Authors: | George Tzavelas Demosthenes Panagiotakos |
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Affiliation: | 1. Department of Statistics and Insurance Science , University of Piraeus , 80 Karaoli &2. Dimitriou str. 185-34, Piraeus , Greece tzafor@unipi.gr;4. Group of Biostatistics, Epidemiology and Research Methods, Department of Nutrition-Dietetics , Harokopio University , 70 El. Venizelou, 17671 , Athens , Greece |
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Abstract: | In this paper, statistical inferences for the size-biased Weibull distribution in two different cases are drawn. In the first case where the size r of the bias is considered known, it is proven that the maximum-likelihood estimators (MLEs) always exist. In the second case where the size r is considered as an unknown parameter, the estimating equations for the MLEs are presented and the Fisher information matrix is found. The estimation with the method of moments can be utilized in the case the MLEs do not exist. The advantage of treating r as an unknown parameter is that it allows us to perform tests concerning the existence of size-bias in the sample. Finally a program in Mathematica is written which provides all the statistical results from the procedures developed in this paper. |
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Keywords: | Weibull distribution weighted distribution maximum-likelihood estimator method of moments |
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