On nonlinear weighted total least squares parameter estimation problem for the three-parameter Weibull density

被引：19
作者：
Markovic, Darija [1 ]
Jukic, Dragan [1 ]
机构：
[1] Univ Osijek, Dept Math, HR-31000 Osijek, Croatia
来源：
APPLIED MATHEMATICAL MODELLING | 2010年 / 34卷 / 07期
关键词：
Three-parameter Weibull density; Total least squares; Total least squares estimate; Existence problem; Data fitting; EXISTENCE; MODELS;
D O I：
10.1016/j.apm.2009.10.001
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
The three-parameter Weibull density function is widely employed as a model in reliability and lifetime studies. Estimation of its parameters has been approached in the literature by various techniques, because a standard maximum likelihood estimate does not exist. In this paper we consider the nonlinear weighted total least squares fitting approach. As a main result, a theorem on the existence of the total least squares estimate is obtained, as well as its generalization in the total l(q) norm (q >= 1). Some numerical simulations to support the theoretical work are given. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码：1839 / 1848
页数：10
相关论文
共 26 条
  • [1] Estimating the parameters of Weibull distribution using simulated annealing algorithm
    Abbasi, Babak
    Jahromi, Abdol Hamid Eshragh
    Arkat, Jamal
    Hosseinkouchack, Mehdi
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 183 (01) : 85 - 93
  • [2] [Anonymous], 1988, Parameter estimation in reliability and life span models
  • [3] Bates D. M., 1988, NONLINEAR REGRESSION, DOI DOI 10.1002/9780470316757
  • [4] Bjorck A., 1996, NUMERICAL METHODS LE, DOI DOI 10.1137/1.9781611971484
  • [5] A STABLE AND EFFICIENT ALGORITHM FOR NONLINEAR ORTHOGONAL DISTANCE REGRESSION
    BOGGS, PT
    BYRD, RH
    SCHNABEL, RB
    [J]. SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1987, 8 (06): : 1052 - 1078
  • [6] BURRIDGE J, 1981, J ROY STAT SOC B MET, V43, P41
  • [7] Fuller W. A., 2009, Measurement error models
  • [8] Gill P. E., 1981, Practical optimization
  • [9] AN ANALYSIS OF THE TOTAL LEAST-SQUARES PROBLEM
    GOLUB, GH
    VANLOAN, CF
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1980, 17 (06) : 883 - 893
  • [10] Partial linearization of one class of the nonlinear total least squares problem by using the inverse model function
    Jukic, D
    Scitovski, R
    Späth, H
    [J]. COMPUTING, 1999, 62 (02) : 163 - 178
123