Genelleştirilmiş Lojistik Büyüme Eğrisinin Birinci Türevinin Fourier Dönüşümü

Genelleştirilmiş lojistik büyüme eğrisi simetrisi olmayan sigmoid eğrileri için tipik bir örnektir ve genellikle lineer olmayan regresyon için kullanılır. Bir sigmoid eğrisinin “kritik noktası” kısaca, türevlerinin mutlak ekstremum noktalarının (eğer varsa) limiti olarak tanımlanır. Bir sigmoid eğrisinin kritik noktasının varlığı ve konumu Fourier dönüşümü ile ifade edilebilir. Bu çalışmada, genelleştirilmiş lojistik büyüme eğrisinin birinci türevinin Gama fonksiyonları cinsinden Fourier dönüşümü elde edilmiş ve bazı özel durumlar tartışılmıştır.

Anahtar Kelimeler:

Lojistik büyüme, Fourier dönüşümü, Sigmoid eğrisi

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

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.

Keywords:

Logistic growth, Fourier transform, Sigmoidal curve,

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