Perturbative method for maximum likelihood estimation of the Weibull distribution parameters
The two-parameter Weibull distribution is the predominant distribution in reliability and lifetime data analysis. The classical approach for estimating the scale \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}...
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| Format: | Online |
| Language: | English |
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Springer International Publishing
2016
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| Online Access: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5069269/ |
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pubmed-5069269 |
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oai_dc |
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pubmed-50692692016-11-03 Perturbative method for maximum likelihood estimation of the Weibull distribution parameters Coria, V. H. Maximov, S. Rivas-Dávalos, F. Melchor-Hernández, C. L. Research The two-parameter Weibull distribution is the predominant distribution in reliability and lifetime data analysis. The classical approach for estimating the scale \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\alpha )$$\end{document}(α) and shape \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\beta )$$\end{document}(β) parameters employs the maximum likelihood estimation (MLE) method. However, most MLE based-methods resort to numerical or graphical techniques due to the lack of closed-form expressions for the Weibull \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}β parameter. A Weibull \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}β parameter estimator based on perturbation theory is proposed in this work. An explicit expression for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}β is obtained, making the estimation of both parameters straightforward. Several right-censored lifetime data sets with different sample sizes and censoring percentages were analyzed in order to assess the performance of the proposed estimator. Study case results show that our parameter estimator provides solutions of high accuracy, overpassing limitations of other parameter estimators. Springer International Publishing 2016-10-18 /pmc/articles/PMC5069269/ /pubmed/27812442 http://dx.doi.org/10.1186/s40064-016-3500-y Text en © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| repository_type |
Open Access Journal |
| institution_category |
Foreign Institution |
| institution |
US National Center for Biotechnology Information |
| building |
NCBI PubMed |
| collection |
Online Access |
| language |
English |
| format |
Online |
| author |
Coria, V. H. Maximov, S. Rivas-Dávalos, F. Melchor-Hernández, C. L. |
| spellingShingle |
Coria, V. H. Maximov, S. Rivas-Dávalos, F. Melchor-Hernández, C. L. Perturbative method for maximum likelihood estimation of the Weibull distribution parameters |
| author_facet |
Coria, V. H. Maximov, S. Rivas-Dávalos, F. Melchor-Hernández, C. L. |
| author_sort |
Coria, V. H. |
| title |
Perturbative method for maximum likelihood estimation of the Weibull distribution parameters |
| title_short |
Perturbative method for maximum likelihood estimation of the Weibull distribution parameters |
| title_full |
Perturbative method for maximum likelihood estimation of the Weibull distribution parameters |
| title_fullStr |
Perturbative method for maximum likelihood estimation of the Weibull distribution parameters |
| title_full_unstemmed |
Perturbative method for maximum likelihood estimation of the Weibull distribution parameters |
| title_sort |
perturbative method for maximum likelihood estimation of the weibull distribution parameters |
| description |
The two-parameter Weibull distribution is the predominant distribution in reliability and lifetime data analysis. The classical approach for estimating the scale \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$(\alpha )$$\end{document}(α) and shape \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$(\beta )$$\end{document}(β) parameters employs the maximum likelihood estimation (MLE) method. However, most MLE based-methods resort to numerical or graphical techniques due to the lack of closed-form expressions for the Weibull \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\beta$$\end{document}β parameter. A Weibull \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\beta$$\end{document}β parameter estimator based on perturbation theory is proposed in this work. An explicit expression for \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\beta$$\end{document}β is obtained, making the estimation of both parameters straightforward. Several right-censored lifetime data sets with different sample sizes and censoring percentages were analyzed in order to assess the performance of the proposed estimator. Study case results show that our parameter estimator provides solutions of high accuracy, overpassing limitations of other parameter estimators. |
| publisher |
Springer International Publishing |
| publishDate |
2016 |
| url |
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5069269/ |
| _version_ |
1613688373433597952 |