engleski

Solution of the least-squares problem for logistic function

Given the data (p_i, t_i, f_i), i=1, ..., m, m>3, we consider the best least squares approximation of parameters for the logistic function t\mapsto f(t ; alpha, beta, gamma)=\frac{; ; ; alpha}; ; ; {; ; ; 1+e^{; ; ; beta - gamma t}; ; ; }; ; ; , alpha, gamma>0, beta\in\R. We give necessary and sufficient conditions which guarantee the existence of such optimal parameters.

nonlinear least squares; logistic function; existence problem

nije evidentirano