New Estimators for Weibull Distribution Parameters: Comprehensive Comparative Study for Weibull Distribution

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Sadani Sahar; ABDOLLAHNEZHAD KAMEL; Teimouri Mahdi; RANJBAR VAHID

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Journal Paper

Paper Information

Journal: JOURNAL OF STATISTICAL RESEARCH OF IRAN (JSRI) Year:2019 | Volume:16 | Issue:1 Page(s): 33-57

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Title

New Estimators for Weibull Distribution Parameters: Comprehensive Comparative Study for Weibull Distribution

Author(s)

Sadani Sahar | ABDOLLAHNEZHAD KAMEL | Teimouri Mahdi | RANJBAR VAHID

Keywords

Generalized least square

$L$-moment

logarithmic moment

maximum likelihood estimator

$U$-statistic

Weibull distribution

weighted least square

weighted maximum likelihood.

Abstract

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.

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APA: Copy

Sadani, Sahar, ABDOLLAHNEZHAD, KAMEL, Teimouri, Mahdi, & RANJBAR, VAHID. (2019). New Estimators for Weibull Distribution Parameters: Comprehensive Comparative Study for Weibull Distribution. JOURNAL OF STATISTICAL RESEARCH OF IRAN (JSRI), 16(1), 33-57. SID. https://sid.ir/paper/779545/en

Vancouver: Copy

Sadani Sahar, ABDOLLAHNEZHAD KAMEL, Teimouri Mahdi, RANJBAR VAHID. New Estimators for Weibull Distribution Parameters: Comprehensive Comparative Study for Weibull Distribution. JOURNAL OF STATISTICAL RESEARCH OF IRAN (JSRI)[Internet]. 2019;16(1):33-57. Available from: https://sid.ir/paper/779545/en

IEEE: Copy

Sahar Sadani, KAMEL ABDOLLAHNEZHAD, Mahdi Teimouri, and VAHID RANJBAR, “New Estimators for Weibull Distribution Parameters: Comprehensive Comparative Study for Weibull Distribution,” JOURNAL OF STATISTICAL RESEARCH OF IRAN (JSRI), vol. 16, no. 1, pp. 33–57, 2019, [Online]. Available: https://sid.ir/paper/779545/en

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