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On the choice of initial approximation of the least squares estimate in some growth models of exponential type

In this paper we consider the least squares fitting of the some popular nonlinear growth curve models of exponential type: 3-parametric exponential, logistic and Gompertz curve. Numerical methods for minimizing the corresponding sum of squares require an initial approximation which is as good as possible. Using the fact that the observed values must clearly be close in some sense to the corresponding exact values, we propose a choice of a good initial approximation. The idea is illustrated by numerical examples.

3-parametric exponential function; logistic function; Gompertz function; nonlinear least squares; least squares estimate; initial approximation

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