Dragan Jukić

On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution

The problem of nonlinear weighted least squares fitting of the three-parameter Weibull distribution to the given data (wi,ti,yi), i=1,...,n, is considered. The part wi>0 of the data stands for the data weights. It is shown that the best least squares estimate exists provided that the data satisfy just the following two natural conditions: (i) 0

Existence of optimal solution for exponential model by least squares

In this paper we prove the existence theorem for the best least squares approximation of the optimal parameters for the exponential model function. We give sufficient conditions which guarantee the existence of such optimal parameters. Using these results and methods, we are able to localize a sufficiently narrow area where one can choose a good initial approximation.

A method for solving the parameter identification problem for ordinary differential equations of the second order

We give a method for solving the parameter identification problem for ordinary differential equations of the second order using a noninterpolated moving least squares method. The method is tested in two practical examples.

Partial linearization of one class of the nonlinear total least squares problem by using the inverse model function

Abstract.In this paper we consider a special nonlinear total least squares problem, where the model function is of the form

The existence of optimal parameters of the generalized logistic function

f(x;a,b)=\phi^{-1}(ax+b)

On nonlinear weighted errors-in-variables parameter estimation problem in the three-parameter Weibull model

. Using the fact that after an appropriate substitution, the model function becomes linear in parameters, and that the symmetry preserves the distances, this nonlinear total least squares problem can be greatly simplified. In this paper we give the existence theorem, propose an efficient algorithm for searching the parameters and give some numerical examples.

THE BEST LEAST SQUARES APPROXIMATION PROBLEM FOR A 3-PARAMETRIC EXPONENTIAL REGRESSION MODEL

The estimation of optimal parameters in a mathematical model described by the generalized logistic function with saturation level A and the asymmetry coefficient γ is a nonlinear least squares problem. In this paper we prove the existence of optimal parameters under considerably weaker conditions than those required in [1].

Total least-squares problem for exponential function

This paper is concerned with the three-parameter Weibull distribution which is widely used as a model in reliability and lifetime studies. In practice, the Weibull model parameters are not known in advance and must be estimated from a random sample. Difficulties in applying the method of maximum likelihood to three-parameter Weibull models have led to a variety of alternative approaches in the literature. In this paper we consider the nonlinear weighted errors-in-variables (EIV) fitting approach. As a main result, two theorems on the existence of the EIV estimate are obtained. An illustrative example is also included.

Total least squares fitting Bass diffusion model

(Received 13 February 1997)AbstractGiven the data (p,-, f,,/,) i, = 1,... ,m, we consider the existence problem for the best leastsquares approximatio onf parameter fos r the 3-parametri c exponential regression model.This problem doe nos t always have a solution. In this paper it is shown that this problemhas a solution provided that the data are strongly increasin atg the ends.

On parameter estimation in the bass model by nonlinear least squares fitting the adoption curve

Given the data , i = 1,...,m, we consider the existence problem for the optimal parameters for the exponential function approximating these data in the sense of total least squares. We give sufficient conditions which guarantee the existence of such optimal parameters.