Least-squares fitting Gompertz curve
Journal of Computational and Applied Mathematics
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Criteria for global minimum of sum of squares in nonlinear regression
Computational Statistics & Data Analysis
Computational Statistics & Data Analysis
Application of gradient descent method to the sedimentary grain-size distribution fitting
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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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.