Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start
| Autor: | Dragan Jukić, Mirta Benšić, Darija Marković |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
0209 industrial biotechnology
Mathematical optimization Estimation theory Applied Mathematics Nonparametric statistics Three-parameter Weibull density 02 engineering and technology Generalized least squares 01 natural sciences Least squares 010104 statistics & probability Nonlinear system Computational Mathematics 020901 industrial engineering & automation Existence problem Data fitting Non-linear least squares Curve fitting Applied mathematics Nonlinear least squares 0101 mathematics Least squares estimate three-parameter Weibull density data fitting nonlinear least squares least squares estimate existence problem Weibull distribution Mathematics |
| Zdroj: | Journal of Computational and Applied Mathematics. 228(1):304-312 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2008.09.025 |
| Popis: | This paper is concerned with the parameter estimation problem for the three-parameter Weibull density which is widely employed as a model in reliability and lifetime studies. Our approach is a combination of nonparametric and parametric methods. The basic idea is to start with an initial nonparametric density estimate which needs to be as good as possible, and then apply the nonlinear least squares method to estimate the unknown parameters. As a main result, a theorem on the existence of the least squares estimate is obtained. Some simulations are given to show that our approach is satisfactory if the initial density is of good enough quality. |
| Databáze: | OpenAIRE |
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