The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve

Abstract

The “generalized logistic growth curve” or the “5-point sigmoid” is a typical example for sigmoidal curves without symmetry and it is commonly used for non-linear regression. The “critical point” of a sigmoidal curve is defined as the limit, if it exists, of the points where its derivatives reach their absolute extreme values. The existence and the location of the critical point of a sigmoidal curve is expressed in terms of its Fourier transform. In this work, we obtain the Fourier transform of the first derivative of the generalized logistic growth curve in terms of Gamma functions and we discuss special cases.