Total Least Squares Problem for the Hubbert Function

In this paper we consider the parameter estimation (PE) problem for the logistic function-model in case when it is not possible to measure its values. We show that the PE problem for the logistic function can be reduced to the PE problem for its derivative known as the Hubbert function. Our proposed method is based on finite differences and the total least squares method.

[1]  H. Schwetlick,et al.  Numerical Methods for Estimating Parameters in Nonlinear Models With Errors in the Variables , 1985 .

[2]  Christopher J. Easingwood,et al.  Early product life cycle forms for infrequently purchased major products , 1987 .

[3]  Rudolf Scitovski,et al.  THE BEST LEAST SQUARES APPROXIMATION PROBLEM FOR A 3-PARAMETRIC EXPONENTIAL REGRESSION MODEL , 2000 .

[4]  Rudolf Scitovski,et al.  Solution of the least-squares problem for logistic function , 2003 .

[5]  M. Hubbert,et al.  Nuclear energy and the fossil fuels , 1956 .

[6]  Eugene Demidenko.  On the existence of the least squares estimate in nonlinear growth curve models of exponential type , 1996 .

[7]  Rudolf Scitovski,et al.  Solving parameter estimation problem in new product diffusion models , 2002, Appl. Math. Comput..

[8]  Philip E. Gill,et al.  Practical optimization , 1981 .

[9]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[10]  Rudolf Scitovski,et al.  The existence of optimal parameters of the generalized logistic function , 1996 .

[11]  Sabine Van Huffel,et al.  The total least squares problem , 1993 .

[12]  Gene H. Golub,et al.  An analysis of the total least squares problem , 1980, Milestones in Matrix Computation.

[13]  Helmuth Späth,et al.  Partial Linearization of One Class of the Nonlinear Total Least Squares Problem by Using the Inverse Model Function , 1999, Computing.

[14]  Åke Björck,et al.  Numerical methods for least square problems , 1996 .

[15]  Rudolf Scitovski,et al.  Total least-squares problem for exponential function , 1996 .

[16]  P. Boggs,et al.  A Stable and Efficient Algorithm for Nonlinear Orthogonal Distance Regression , 1987 .

[17]  J. Nelder.  The Fitting of a Generalization of the Logistic Curve , 1961 .

[18]  Rudolf Scitovski,et al.  Existence results for special nonlinear total least squares problem , 1998 .

[19]  David A. Ratkowsky,et al.  Handbook of nonlinear regression models , 1990 .

[20]  Rudolf Lewandowski.  Prognose- und Informationssysteme : und ihre Anwendungen , 1974 .