[A contribution to the generalization of the Gompertz function].
SCHARF (1976) discusses various growth models. For the Gompertz function the differential equation (Formula: see text) is used. In words: the difference between relative growth rate and relative growth acceleration is constant. On the other hand, according to WENK (1973), the differential equation (Formula: see text) applies to the Gompertz function. It can be shown mathematically that (Formula: see text) applies in general. From Eq. (2) one obtains without trouble (Formula: see text). Therefore, the property leading to the Gompertz function may be defined as follows; the logarithmic derivation of the relative growth rate is constant. Eq. (2) is applicable only in special cases. It can be extended by assuming that c is not constant, but a function of time. In this way, a great number of growth functions can be found, which have to be regarded as model-based extensions of the Gompertz function.
D000818:Animals; D006128:Growth; D006801:Humans; D008433:Mathematics; D008954:Models, Biological
Ein Beitrag zur Verallgemeinerung der Gompertz-Funktion.