Solution of the least-squares problem for logistic function

Authors:
D. Jukic´;R. Scitovski
Affiliations:
Department of Mathematics, University J.J. Strossmayer, Gajev trg 6, HR-31000 Osijek, Croatia;Department of Mathematics, University J.J. Strossmayer, Gajev trg 6, HR-31000 Osijek, Croatia
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

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Abstract

Given the data (pi, ti, fi), i= 1,...., m, m 3, we consider the best least-squares approximation of parameters for the logistic function t ↦ f(t;α,β,γ)= α/(1 + eβ-γt), α, γ 0, β ∈ R. We give necessary and sufficient conditions which guarantee the existence of such optimal parameters.