engleski

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. Given the data $(p_i, t_i, y_i)$, $i=1, \ldots, m$, $m>3$, we give necessary and sufficient conditions which guarantee the existence of the total least squares estimate of parameters for the Hubbert function, suggest a choice of a good initial approximation and give some numerical examples.

logistic function; Hubbert function; nonlinear least squares; total least squares; existence problem

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