Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start
type: Item
instance of: scholarly article
title: Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start
zbMATH Open document ID: 1175.65017
author: Darija Marković
author: Dragan Jukić
author: Mirta Benšić
published in: Journal of Computational and Applied Mathematics
publication date: 2009-05-28T00:00:00Z
review text: The authors consider a three parameter Weibull distribution with a density \(f(x;\alpha,\beta,\eta)\) and wish to estimate its parameters. The main improvement over the previously suggested methods is the proposal to combine parametric and nonparametric estimators in the following way. First, a nonparametric estimator \(\hat f\) is constructed from the data \(\{t_i\}\) and the values of \(y_i=\hat f(t_i)\) are evaluated. Second, the parameters \(\alpha,\beta,\eta\) are estimated as \[ \arg\min_{\alpha>0,\beta\geq0,\eta\geq0}\;\sum_{i=1}^{n}w_i\big[y_i-f(t_i;\alpha,\beta,\eta)\big]^2, \] where \(w_i\) are the data weights describing the assumed relative accuracy of the data. The main result of the paper, Theorem~1, guarantees the existence of such a solution. A small simulation study completes the paper.
reviewed by: Jaromír Antoch
Mathematics Subject Classification ID: 65C60
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 62N05
Mathematics Subject Classification ID: 62F10
zbMATH DE Number: 5559057
zbMATH Keywords: nonlinear weighted least squares
zbMATH Keywords: three parameter Weibull distribution data fitting
zbMATH Keywords: least squares estimate
zbMATH Keywords: nonparametric estimator
MaRDI profile type: Publication
full work available at URL: j.cam.2008.09.025
OpenAlex ID: W1990155951
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DOI: 10.1016/J.CAM.2008.09.025
description: scientific article; zbMATH DE number 5559057