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JSRI 2019, 16(1): 33-57 Back to browse issues page
New Estimators for Weibull Distribution Parameters: Comprehensive Comparative Study for Weibull Distribution
Sahar Sadani, Kamel Abdollahnezhad *1, Mahdi Teimouri, Vahid Ranjbar
1- , k.abdollahnezhad@gu.ac.ir
Abstract:   (246 Views)
 
In this paper we focus on two topics. Firstly, we propose $U$-statistics for the Weibull distribution parameters. The consistency and asymptotically normality of the introduced $U$-statistics are proved theoretically and by simulations. Several of methods have been proposed for estimating the parameters of Weibull distribution in the literature. These methods include: the generalized least square type 1, the generalized least square type 2, the $L$-moments, the Logarithmic moments, the maximum likelihood estimation, the method of moments, the percentile method, the weighted least square, and weighted maximum likelihood estimation. Secondly, due to lack of a comprehensive comparison between the Weibull distribution parameters estimators, a comprehensive comparison study is made between our proposed $U$-statistics and above nine estimators. In our knowledge, this work is the most comprehensive comparison study for the estimators for the Weibull distribution. Based on simulations, it turns out that different estimators may appeal for different range of the parameters. So, practitioners are allowed to chose the best estimator that is suggested by the goodness-of-fit criteria.
 
 
Keywords: Generalized least square, $L$-moment, logarithmic moment, maximum likelihood estimator, $U$-statistic, Weibull distribution, weighted least square, weighted maximum likelihood.
Full-Text [PDF 2495 kb]   (81 Downloads)    
Type of Study: Research | Subject: General
Received: 2019/07/20 | Accepted: 2020/10/7 | Published: 2019/09/19
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sadani S, abdollahnezhad K, teimouri M, ranjbar V. New Estimators for Weibull Distribution Parameters: Comprehensive Comparative Study for Weibull Distribution. JSRI. 2019; 16 (1) :33-57
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مجله‌ی پژوهش‌های آماری ایران (علمی - پژوهشی) Journal of Statistical Research of Iran JSRI
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